Important
Version 3.2.2.3 is released!
OpenSeesPy is on PyPi (Windows, Linux).
OpenSeesPy is official in DesignSafe (Webbased).
OpenSeesPy can now run on Windows Subsystem for Linux (Windows).
The latest version of this document can be found at https://openseespydoc.readthedocs.io/en/latest/.
Note
Questions including modeling issues and the use of OpenSeesPy, please post on OpenSeesPy Forum or send issues to <OpenSeesPy Github
You are very welcome to contribute to OpenSeesPy with new command documents and examples by sending pull requests through github pulls.
For errors in this document, submit on github issues.
The OpenSeesPy LibraryÂ¶
OpenSeesPy is a Python 3 interpreter of OpenSees. A minimum script is shown below:
# import OpenSeesPy
import openseespy.opensees as ops
# import OpenSeesPy plotting commands
import openseespy.postprocessing.Get_Rendering as opsplt
# wipe model
ops.wipe()
# create model
ops.model('basic', 'ndm', 2, 'ndf', 3)
# plot model
opsplt.plot_model()
To run a test of the pip installation:
pytest pyargs openseespy.test
DeveloperÂ¶
Minjie Zhu <email>
InstallationÂ¶
PyPi (Windows, Linux)Â¶
In Jupyter NotebookÂ¶
In command line (optional)Â¶
To install
python m pip install openseespy python m pip install user openseespy
To upgrade
python m pip install upgrade openseespy python m pip install user upgrade openseespy
To import
import openseespy.opensees as ops
DesignSafe (Webbased)Â¶
OpenSeesPy has been offical in DesignSafe.
OpenSeesPy in DesignSafeÂ¶
Follow steps below to run OpenSeesPy in DesignSafe.
Tip
 Go To DesignSafe website and click register
Tip
 Register an account for free and log in
Tip
 Land on your own portal and go to workspace
Tip
 In your workspace, select
Jupyter
, launch it, and start my server
Tip
 Now you should be in the
Jupyter
Notebook  Go to
mydata
and alwasy save your data under this folder
Tip
 In the
mydata
folder, selectNew
and thenPython 3
Tip
 The OpenSeesPy version on DesignSafe is not the latest.
 To update to the latest and import:
Tip
 Now you can write OpenSeesPy script in
Jupyter
Notebook, run the script, and show results  To show figure in the Notebook, you should include
%matplotlib inline
at the beginning
Paraview in DesignSafeÂ¶
DesignSafe provides paraview for viewing OpenSeesPy results:
Tip
 Make sure the steps in OpenSeesPy in DesignSafe are completed.
Tip
 Go to
Workspace
and selectVisualizaion
andParaview
.
Tip
 In the Job Submission windows, you should select
Working Directory
,Maximum job runtime
,Job name
, andNode Count
, and clickRun
.
Tip
 You can see the job status on the right
Tip
 Wait until see this windows and connect to Paraview
Tip
 Now open the pvd file in Paraview
Tip
 Initially, you see nothing
 Check the
Pipeline Browser
 Click on the eye left to the file in
Pipeline Browser
Tip
 Change the
Solid Color
to other variables  Change
Surface
toSurface With Edges
Windows Subsystem for Linux (Windows)Â¶
This is a real Linux subsystem for you to run OpenSeesPy Linux version on Windows.
Install the Windows Subsystem for LinuxÂ¶
Follow the instruction on here to install Windows Subsystem for Linux on Windows 10. There are a couple of Linux distributions available and Ubuntu is recommended. Once the Linux is installed, it will show as an application in the start menu.
Install Anaconda and start Jupyter NotebookÂ¶
Run the subsystem from start menu and a terminal window will show.
Download Anaconda Linux version with command
~$ wget https://repo.anaconda.com/archive/Anaconda32019.10Linuxx86_64.sh
Install Anconda Linux version with commands
~$ bash Anaconda32019.10Linuxx86_64.sh >>> Please answer 'yes' or 'no': >>> yes >>> Anaconda3 will not be installed into this location: [/home/username/anaconda3] >>> (enter)
Start Jupyter Notebook
~$ /home/username/anaconda3/bin/jupyternotebook
Copy the address in red box to a web browser
In Jupyter NotebookÂ¶
Start a new notebook and then
In the command line (optional)Â¶
Run Anaconda with following command, where username is your username of your computer. Please use the username shown in last step
~$ /home/username/anaconda3/bin/python3.7
Install or Upgrade OpenSeesPy with commands
~$ /home/username/anaconda3/bin/python3.7 m pip install openseespy ~$ /home/username/anaconda3/bin/python3.7 m pip install upgrade openseespy
Run OpenSeesPy
First run Anaconda with
~$ /home/username/anaconda3/bin/python3.7
Then import OpenSeesPy with
import openseespy.opensees as ops ops.printModel()
run OpenSeesPy scripts
/home/username/anaconda3/bin/python3.7 script.py
CompilationÂ¶
Compilation for MacÂ¶
Following is the OpenSees Compilation using QT by
Stevan Gavrilovic github
Original instructions can be found at here.
A Qt build environment for OpenSeesÂ¶
OpenSeesQt
A Qt build environment for OpenSees â Open System For Earthquake Engineering Simulation Pacific Earthquake Engineering Research Center(http://opensees.berkeley.edu).
Qt is an open source, crossplatform development environment that is free for many uses. Please see the license.
DependencyÂ¶
The purpose of this project is to create a package that will allow aspiring developers to get started on writing code without having to worry about the compilation environment. A program as large as OpenSees relies on many thirdparty libraries, often referred to as dependencies. It can be a daunting task assembling, compiling, and linking these libraries. Many times, these libraries depend on other libraries, and so on. The current list of dependencies includes:
 MUMPS (5.1.2)
 Scalapack (2.0.2.13)
 UMFPACK (5.7.7) contained in SuiteSparse (5.3.0)
 SUPERLU (5.2.1)
 SUPERLUMT (3.0)
 SUPERLUDIST (5.1.0)
 Openblas (0.3.5)
 Parmetis (4.0.3)
 ARPACK (3.6.3)
 Libevent (2.1.8)
 GCC(8.2.0)
 TCL (8.6.9)** Tcl only
 Python(3.7.2)** OpenSeesPy only
Please ensure that your project complies with each libraryâs licensing requirements.
Another feature of this build platform is modularity. Developers can select from a list of build options that can be turned on and off as required. The basic configuration builds the structural analysis core. Other build options include parallel processing, reliability, and the particle finite element method (PFEM) modules. Python and Tcl interpreters are additional build options. These options are located in single configuration file called qmake.conf. By default, the environment is configured to build the core along with the parallel processing module. Other options can be turned on by deleting the â#âsymbol that precedes the option; this includes the option into the build environment.
Note
Note: This build environment comes with precompiled dependencies. Although this makes getting started easier, the caveat is that your build environment (compiler version) must match that of the environment used to compile the dependencies. The supported environments are listed below. There are no guarantees that it will work with other build environments. In other words, make sure your compiler type and version (i.e., clang1000.11.45.5) matches the version below listed under the heading âSupported Build Environmentsâ. Otherwise, bad things might happen. Also, this project is still a work in progress. Currently, only building in OS X is supported. Windows support will be added shortly. Moreover, not all build options are supported. For example, compiling with fortran is not supported.
Note
This project uses qmake and Qt Creator. qmake is a build tool for compiling and linking applications. Qt Creator is a free IDE (interactive development environment) that bundles code writing/editing and application building within one program. Qt Creator uses project (.pro) files. The project files contain all information required by qmake to build an application.
Getting started:Â¶
 Download and install Qt open source from https://www.qt.io/download The version of the Qt library is not important in this case since the library is not used in the OpenSees project (although I use Qt in other projects and recommend it)
 Download the OpenSeesQt source code into a folder of your choice (https://github.com/steva44/OpenSees/archive/master.zip)
 In the directory containing the code, double click on the âOpenSees.proâ file. If compiling OpenSeesPy, open the âOpenSeesPy.proâ file. The .pro files are project files that will automatically open the project in Qt Creator.
 Select a build configuration, for example âDesktop Qt 5.12.1 clang 64bitâ. The project will automatically configure itself. You only have to do this once.
 The lefthand pane should now display the project directory structure. In the lefthand pane, under the heading qmake, open the âqmake.confâ file. Review and select additional build options, if any. Note that this is still a work in progress and not all build options are supported.
 Click on the âstartâ button in the bottom lefthand corner of Qt Creator to compile. Clicking on the small computer symbol above the start button allows for switching between the debug and release deploy configurations. The release deployment results in faster program execution but it does not allow for debugging or stepping through the code. The start button with the bug symbol opens the debugger.
 Go and have a coffee, it will take a few minutes to finish compiling!
Building OpenSeesPy:Â¶
OpenSeesPy builds OpenSees as a library object that can be used within Python.
Steps: Follow steps 14 under the heading getting started above.
The lefthand pane should now display the project directory structure. In the lefthand pane, under the heading qmake, open the âqmake.confâ file. Under the heading #INTERPRETERS, uncomment the _PYTHON option by removing the â#â symbol. Everything else should be configured automatically going forward. Python automatically compiles with the reliability, parallel, and PFEM modules.
The last few lines at the end of the âOpenSeesPy.proâ file contain the location of the Python framework. Update this so that it matches the location of Python on your build system.
Click on the âstartâ button in the bottom lefthand corner of Qt Creator to start compiling. Clicking on the small computer symbol allows for switching between the debug and release deploy configurations. The release deployment results in faster program execution but it does not allow for debugging or stepping through the code. Build in release mode if using OpenSees as a library in a Python project.
Go and have a coffee, it will take a few minutes to finish compiling!
After successful compilation, the library will be in the âbinâ folder. The bin folder is located in the âbuildâ folder which is created, by default, one directory higher than the OpenSeesQt source code. The name of the build folder should look something like this: buildOpenSeesPyDesktop_Qt_5_12_1_clang_64bitDebug
OS X only
OS X automatically prepends a âlibâ to the library file. Remove this âlibâ and rename the file to be âopensees.dylibâ Next, a symbolic link is required for a Python project to import the library. To create a symbolic link, cd the directory containing the OpenSees library in terminal and run the following command to create a symbolic link:
ln s opensees.dylib opensees.so
There should now be a .so (shared object) file in addition to the .dylib file. Finally, copy both the .dylib and the .so âlinkâ into your python environment folder to import it into your project. Directions for using OpenSeesPy can be found at the project website: https://openseespydoc.readthedocs.io/en/latest/index.html
Supported Build Environments:Â¶
OSX
Build Environment:
 OSX 10.14.3 (Mojave)
 Qt 5.12.1
 Qt Creator 4.8.1
Compiler:
 Apple LLVM version 10.0.0 (clang1000.11.45.5)
 Target: x86_64appledarwin18.2.0
 Thread model: posix 64BIT architecture
To find the version of clang on your computer, type the following in terminal:
clang version
Note
This project comes with prebuilt libraries for everything except Python. Therefore, you do not have to go through the trouble of building any libraries unless you are using a special build system or you want to experiment. The precompiled library files are located in the âOpenSeesLibsâ folder. In the event that you are feeling adventurous and you want to compile the libraries on your own, instructions are given below for each library, for each operating system. After successful compilation, note the installation directory. This directory contains the locations of the âincludeâ and âlibâ folders for that library. If replacing or adding new libraries, the file paths should be updated in the âOpenSeesLibs.priâ file. This is required so that the compiler knows where to find the header files and to link the libraries to your project.
OSX
On OSX, the dependencies are built/installed with Homebrew. Homebrew is a free and opensource software package management system that simplifies the installation of software on Appleâs macOS operating system and Linux. Homebrew maintains its own folder within /usr/local/
directory aptly named the 'Cellar'
:
/usr/local/Cellar/
Each dependency installed through Homebrew will have its own subfolder within the Cellar directory. Each subfolder contains that dependencies 'include'
and 'lib'
folders.
MUMPSÂ¶
MUltifrontal Massively Parallel sparse direct Solver, or MUMPS, is a sparse direct solver used for parallel solving of a system of equations
Installing MUMPS via brew: Dominique Orban has written a Homebrew formula (http://brew.sh) for Mac OSX users. Homebrew MUMPS is now available via the OpenBLAS tap. Build instructions are as follows:
In terminal, copy and paste each command individually and execute:
brew tap dpo/openblas
brew tappin dpo/openblas
brew options mumps # to discover build options
brew install mumps [optionsâŠ]
The options can be left blank, i.e., with default options so the last line will look like:
brew install mumps
Mumps requires the following dependencies that will automatically be installed:
Scalapack
OpenMPIÂ¶
OpenMPI is a high performance message passing library (https://www.openmpi.org/)
Installing OpenMpi via brew: In terminal, copy and paste the following command and execute:
brew install openmpi
OpenMPI requires the following dependencies that will automatically be installed:
 GCC (GNU compiler collection)
 libevent (Asynchronous event library: https://libevent.org/)
UMFPACKÂ¶
UMFPACK is a set of routines for solving unsymmetric sparse linear systems of the form Ax=b, using the Unsymmetric MultiFrontal method (Matrix A is not required to be symmetric). UMFPACK is part of suitesparse library in homebrew/science
In terminal, copy and paste each command individually and execute:
brew tap homebrew/science
brew install suitesparse
UMFPACK requires the following dependencies that will automatically be installed:
 Metis (âMETISâ is a type of GraphPartitioner and numberer  An Unstructured Graph Partitioning And Sparse Matrix Ordering Systemâ, developed by G. Karypis and V. Kumar at the University of Minnesota.
SUPERLUÂ¶
SUPERLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations. The library is written in C and is callable from either C or Fortran program. It uses MPI, OpenMP and CUDA to support various forms of parallelism.
Installing SUPERLU via brew In terminal, copy and paste the following command and execute:
brew install superlu
Should install by default with option withopenmp
enabled. Open MP is needed for parallel analysis.
SUPERLU requires the following dependencies that will automatically be installed:
 GCC (GNU compiler collection)
 openblas (In scientific computing, OpenBLAS is an open source implementation of the BLAS API with many handcrafted optimizations for specific processor types)
SUPERLUMTÂ¶
SUPERLU but for for shared memory parallel machines. Provides Pthreads and OpenMP interfaces.
Installing SUPERLUMT via brew: In terminal, copy and paste the following command and execute:
brew install superlu_mt
SUPERLUMT requires the following dependencies that will automatically be installed:
 openblas
SUPERLUDISTÂ¶
SUPERLU but for for for distributed memory parallel machines. Supports manycore heterogeous node architecture: MPI is used for interprocess communication, OpenMP is used for onnode threading, CUDA is used for computing on GPUs.
Installing SUPERLUDIST via brew: In terminal, copy and paste the following command and execute:
brew install superlu_dist
SUPERLUDIST requires the following dependencies that will automatically be installed:
 GCC (GNU compiler collection)
 openblas (In scientific computing, OpenBLAS is an open source implementation of the BLAS API with many handcrafted optimizations for specific processor types)
 OpenMPI (a high performance message passing library (https://www.openmpi.org/))
 Parmetis (MPI library for graph/mesh partitioning and fillreducing orderings)
LAPACK (SCALAPACK)Â¶
The Linear Algebra PACKage, or LAPACK, is written in Fortran 90 and provides routines for solving systems of simultaneous linear equations, leastsquares solutions of linear systems of equations, eigenvalue problems, and singular value problems.The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision.
LAPACK is given as a system library in OSX, you may have to update the locations of your system library in âOpenSeesLibs.priâ
BLASÂ¶
The BLAS (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations.
BLAS is given as a system library in OSX, you may have to update the locations of your system library in âOpenSeesLibs.priâ
ARPACKÂ¶
ARPACK contains routines to solve large scale eigenvalue problems
Installing ARPACK via brew: In terminal, copy and paste the following command and execute:
brew install arpack
ARPACK requires the following dependencies that will automatically be installed:
 GCC (GNU compiler collection)
 openblas (In scientific computing, OpenBLAS is an open source implementation of the BLAS API with many handcrafted optimizations for specific processor types)
GCCÂ¶
Many of the dependencies require fortran (there is still a lot of legacy fortran code floating around in the engineering world). On OSX, I found the best solution is to use the prebundled fortran capabilities in the GNU compiler collection or GCC. In addition to its fortran capabilities, GCC is a dependency for many other libraries.
Installing GCC via brew: In terminal, copy and paste the following command and execute:
brew install GCC
PYTHONÂ¶
Python is an interpreted, highlevel, generalpurpose programming language. It is used in OpenSees as an interpreter in the OpenSeesPy version. In OpenSeesPy, Python version 3 is used.
Installing PYTHON via brew:
brew install python
MISC. NOTESÂ¶
For the SUPERLU library.
The file supermatrix.h throws an undefined error for the type int_t
. It is actually defined in the file slu_ddefs.h, but for some reason the compiler is not linking the two. Add the following line, copied from slu_ddefs.h to supermatrix.h around line 17:
typedef int int_t; /* default */
Change LogÂ¶
 Version 3.2.2.3 (8/11/2020)
 Fix typos in documentation
 Add testNorm and testIter commands
 Add Python3.7 and Python 3.8 support
 Support latest Anaconda
 Improvements of ploting commands
 ShellDKGT command
 Include OpenSees commits upto 380239c on 8/9
 Version 3.2.2.1 (5/18/2020)
 add gimmeMCK integrator
 Version 3.2.2 (5/8/2020)
 Fix Get_Renderiing tab problem
 Ship with dependent libraries for more Linux systems
 Version 3.2.0 (4.17.2020)
 Add background mesh command
 Add partition command
 Add OpenSeesPy test
 Many bug fixes
 Version 3.1.5.11 (1.10.2020)
 Change versioning method. First two digits match the current OpenSees framework version. The last two digits are the versions for OpenSeesPy.
 For Windows, only support the Python version that corresponds to the current version of Anaconda.
 Add openseespy.postprocessing.Get_Rendering
 Add âinitâ option to Newmark integrator
 Some function can return empty or oneelement lists
 Spaces in string input will be automatically removed
 Bug fixes
 Version 0.5.4
 Support Mac
 Support Python3.7 on Windows and Linux
 Version 0.5.3
 Fix bug in LimitState UniaxialMaterial
 Automatic trimming spaces for string inputs
 Some output commands return lists instead of ints, such as nodeDisp etc.
 Version 0.5.2
 Add package openseespy.postprocessing
 Add setStartNodeTag command
 modalDamping: bug fixes
 Add Steel02Fatiuge material
 Add Concrete02IS material
 Add HardeningMaterial2 material
 Add hystereticBackone command
 Add stiffnessDegradation command
 Add strengthDegradation command
 Add unloadingRule command
 Version 0.4.2019.7
 Parallel: the Linux version is enabled with parallel capability
 Python stream: add no echo
 Mesh: add CorotTruss
 TriMesh: can create line elements
 QuadMesh: can create line and triangular elements
 Python inputs: more flexible input types
 Commands: add ExplicitDifference integrator
 Version 0.3.0
 Add logFile command
 Add partial uniform load fo ForceBeamColumn
 Add ShellDKGT element
 Add âVâ option in Newmark and HHT
 Fix bugs in wipe and Mesh
 Various PFEM updates
 Update to OpenSees 3.0.3
 Version 0.2.0 (8a3d622)
 OpenSeesPy now can print messages and errors in Jupyter Notebook and other Windows based Python applications
 Add setParameter command
 Add nodeDOFs command
 Add setNumThread and getNumThread commands in a multithreaded environment
 Add logFile command
 printA and prinbB can return matrix and vector as lists
 Fix bugs in updateMaterialStage
 PM4Sand improvements
 Add CatenaryCable element to OpenSeesPy
 Version 0.1.1 (f9f45fe)
 Update to OpenSees 3.0.2
 Version 0.0.7 (b75db21)
 Add â2D wheelrailâ element
 PVD recorder allows to set a path
 Add âsdfResponseâ function for single dof dynamic analysis
 Fix a bug in Joint2D
 Fix typo in UCSD UP elements
 Fix bugs in PressureIndependMultiYield
 Add JSON print options to some materials and elements
 Version 0.0.6 (cead6e8)
 Add ânonlinearBeamColumnâ element for backward compatability
 Add âupdateMaterialStageâ function
 Add âRCCircularâ seciton
 Add âquadrâ patch for backward compatibility
 Fix bugs in âSteel01Thermalâ material
 Fix bugs in Truss
 Fix bugs in eleNodes function
 Fix bugs in ZeroLength element
 Fix bugs in FiberSection2d
 Fix bugs in PFEMLinSOE
 Version 0.0.5 (215c63d)
 Update to OpenSees 3.0.0
Model CommandsÂ¶
The model or domain in OpenSees is a collection (an aggregation in objectoriented terms) of elements, nodes, single and multipoint constraints and load patterns. It is the aggregation of these components which define the type of model that is being analyzed.
 model command
 element commands
 node command
 sp constraint commands
 mp constraint commands
 timeSeries commands
 pattern commands
 mass command
 region command
 rayleigh command
 block commands
 beamIntegration commands
 uniaxialMaterial commands
 nDMaterial commands
 section commands
 frictionModel commands
 geomTransf commands
model commandÂ¶
element commandsÂ¶

element
(eleType, eleTag, *eleNodes, *eleArgs)Â¶ Create a OpenSees element.
eleType
(str)element type eleTag
(int)element tag. eleNodes
(list (int))a list of element nodes, must be preceded with *
.eleArgs
(list)a list of element arguments, must be preceded with *
.
For example,
eleType = 'truss'
eleTag = 1
eleNodes = [iNode, jNode]
eleArgs = [A, matTag]
element(eleType, eleTag, *eleNodes, *eleArgs)
The following contain information about available eleType
:
ZeroLength ElementÂ¶
 zeroLength Element
 zeroLengthND Element
 zeroLengthSection Element
 CoupledZeroLength Element
 zeroLengthContact Element
 zeroLengthContactNTS2D
 zeroLengthInterface2D
 zeroLengthImpact3D
zeroLength ElementÂ¶

element
('zeroLength', eleTag, *eleNodes, 'mat', *matTags, 'dir', *dirs, <'doRayleigh', rFlag=0>, <'orient', *vecx, *vecyp>) This command is used to construct a zeroLength element object, which is defined by two nodes at the same location. The nodes are connected by multiple UniaxialMaterial objects to represent the forcedeformation relationship for the element.
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes matTags
(list (int))a list of tags associated with previouslydefined UniaxialMaterials dirs
(list (int))a list of material directions:
 1,2,3  translation along local x,y,z axes, respectively;
 4,5,6  rotation about local x,y,z axes, respectively
rFlag
(float)optional, default = 0 * rFlag
= 0 NO RAYLEIGH DAMPING (default)vecx
(list (float))a list of vector components in global coordinates defining local xaxis (optional) vecyp
(list (float))a list of vector components in global coordinates defining vector yp which lies in the local xy plane for the element. (optional)
rFlag
= 1 include rayleigh damping
Note
If the optional orientation vectors are not specified, the local element axes coincide with the global axes. Otherwise the local zaxis is defined by the cross product between the vectors x and yp vectors specified on the command line.
See also
zeroLengthND ElementÂ¶

element
('zeroLengthND', eleTag, *eleNodes, matTag, <uniTag>, <'orient', *vecx, vecyp>) This command is used to construct a zeroLengthND element object, which is defined by two nodes at the same location. The nodes are connected by a single NDMaterial object to represent the forcedeformation relationship for the element.
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes matTag
(int)tag associated with previouslydefined ndMaterial object uniTag
(int)tag associated with previouslydefined UniaxialMaterial object which may be used to represent uncoupled behavior orthogonal to the plane of the NDmaterial response. SEE NOTES 2 and 3. vecx
(list (float))a list of vector components in global coordinates defining local xaxis (optional) vecyp
(list (float))a list of vector components in global coordinates defining vector yp which lies in the local xy plane for the element. (optional)
Note
 The zeroLengthND element only represents translational response between its nodes
 If the NDMaterial object is of order two, the response lies in the element local xy plane and the UniaxialMaterial object may be used to represent the uncoupled behavior orthogonal to this plane, i.e. along the local zaxis.
 If the NDMaterial object is of order three, the response is along each of the element local exes.
 If the optional orientation vectors are not specified, the local element axes coincide with the global axes. Otherwise the local zaxis is defined by the cross product between the vectors x and yp vectors specified on the command line.
 The valid queries to a zerolength element when creating an ElementRecorder object are âforceâ, âdeformationâ, and âmaterial matArg1 matArg2 âŠâ
See also
zeroLengthSection ElementÂ¶

element
('zeroLengthSection', eleTag, *eleNodes, secTag, <'orient', *vecx, *vecyp>, <'doRayleigh', rFlag>) This command is used to construct a zero length element object, which is defined by two nodes at the same location. The nodes are connected by a single section object to represent the forcedeformation relationship for the element.
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes secTag
(int)tag associated with previouslydefined Section object vecx
(list (float))a list of vector components in global coordinates defining local xaxis (optional) vecyp
(list (float))a list of vector components in global coordinates defining vector yp which lies in the local xy plane for the element. (optional) rFlag
(float)optional, default = 0
rFlag
= 0 NO RAYLEIGH DAMPING (default)rFlag
= 1 include rayleigh damping
See also
CoupledZeroLength ElementÂ¶

element
('CoupledZeroLength', eleTag, *eleNodes, dirn1, dirn2, matTag, <rFlag=1>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes matTag
(float)tags associated with previouslydefined UniaxialMaterial dirn1
dirn2
(int)the two directions, 1 through ndof. rFlag
(float)optional, default = 0
rFlag
= 0 NO RAYLEIGH DAMPING (default)rFlag
= 1 include rayleigh damping
See also
zeroLengthContact ElementÂ¶

element
('zeroLengthContact2D', eleTag, *eleNodes, Kn, Kt, mu, 'normal', Nx, Ny) This command is used to construct a zeroLengthContact2D element, which is Nodetonode frictional contact element used in two dimensional analysis and three dimensional analysis:
eleTag
(int)unique element object tag eleNodes
(list (int))a list of a constrained and a retained nodes Kn
(float)Penalty in normal direction Kt
(float)Penalty in tangential direction mu
(float)friction coefficient

element
('zeroLengthContact3D', eleTag, *eleNodes, Kn, Kt, mu, c, dir) This command is used to construct a zeroLengthContact3D element, which is Nodetonode frictional contact element used in two dimensional analysis and three dimensional analysis:
eleTag
(int)unique element object tag eleNodes
(list (int))a list of a constrained and a retained nodes Kn
(float)Penalty in normal direction Kt
(float)Penalty in tangential direction mu
(float)friction coefficient c
(float)cohesion (not available in 2D) dir
(int)Direction flag of the contact plane (3D), it can be:
 1 Out normal of the master plane pointing to +X direction
 2 Out normal of the master plane pointing to +Y direction
 3 Out normal of the master plane pointing to +Z direction
See also
zeroLengthContactNTS2DÂ¶

element
('zeroLengthContactNTS2D', eleTag, 'sNdNum', sNdNum, 'mNdNum', mNdNum, 'Nodes', *NodesTags, kn, kt, phi) eleTag
(int)unique element object tag sNdNum
(int)Number of Slave Nodes mNdNum
(int)Number of Master nodes NodesTags
(list (int))Slave and master node tags respectively kn
(float)Penalty in normal direction kt
(float)Penalty in tangential direction phi
(float)Friction angle in degrees
Note
 The contact element is nodetosegment (NTS) contact. The relation follows MohrCoulomb frictional law: \(T = N \times \tan(\phi)\), where \(T\) is the tangential force, \(N\) is normal force across the interface and \(\phi\) is friction angle.
 For 2D contact, slave nodes and master nodes must be 2 DOF and notice that the slave and master nodes must be entered in counterclockwise order.
 The resulting tangent from the contact element is nonsymmetric. Switch to the nonsymmetric matrix solver if convergence problem is experienced.
 As opposed to nodetonode contact, predefined normal vector for nodetosegment (NTS) element is not required because contact normal will be calculated automatically at each step.
 contact element is implemented to handle large deformations.
See also
zeroLengthInterface2DÂ¶

element
('zeroLengthInterface2D', eleTag, 'sNdNum', sNdNum, 'mNdNum', mNdNum, 'dof', sdof, mdof, 'Nodes', *NodesTags, kn, kt, phi) eleTag
(int)unique element object tag sNdNum
(int)Number of Slave Nodes mNdNum
(int)Number of Master nodes sdof
,mdof
(int)Slave and Master degree of freedom NodesTags
(list (int))Slave and master node tags respectively kn
(float)Penalty in normal direction kt
(float)Penalty in tangential direction phi
(float)Friction angle in degrees
Note
 The contact element is nodetosegment (NTS) contact. The relation follows MohrCoulomb frictional law: \(T = N \times \tan(\phi)\), where \(T\) is the tangential force, \(N\) is normal force across the interface and \(\phi\) is friction angle.
 For 2D contact, slave nodes and master nodes must be 2 DOF and notice that the slave and master nodes must be entered in counterclockwise order.
 The resulting tangent from the contact element is nonsymmetric. Switch to the nonsymmetric matrix solver if convergence problem is experienced.
 As opposed to nodetonode contact, predefined normal vector for nodetosegment (NTS) element is not required because contact normal will be calculated automatically at each step.
 contact element is implemented to handle large deformations.
See also
zeroLengthImpact3DÂ¶

element
('zeroLengthImpact3D', eleTag, *eleNodes, direction, initGap, frictionRatio, Kt, Kn, Kn2, Delta_y, cohesion) This command constructs a nodetonode zerolength contact element in 3D space to simulate the impact/pounding and friction phenomena.
eleTag
(int)unique element object tag eleNodes
(list (int))a list of a constrained and a retained nodes direction
(int)1
if outnormal vector of master plane points to +X direction2
if outnormal vector of master plane points to +Y direction3
if outnormal vector of master plane points to +Z direction
initGap
(float)Initial gap between master plane and slave plane frictionRatio
(float)Friction ratio in two tangential directions (parallel to master and slave planes) Kt
(float)Penalty in two tangential directions Kn
(float)Penalty in normal direction (normal to master and slave planes) Kn2
(float)Penalty in normal direction after yielding based on Hertz impact model Delta_y
(float)Yield deformation based on Hertz impact model cohesion
(float)Cohesion, if no cohesion, it is zero
Note
 This element has been developed on top of the âzeroLengthContact3Dâ. All the notes available in âzeroLengthContact3Dâ wiki page would apply to this element as well. It includes the definition of master and slave nodes, the number of degrees of freedom in the domain, etc.
 Regarding the number of degrees of freedom (DOF), the end nodes of this element should be defined in 3DOF domain. For getting information on how to use 3DOF and 6DOF domain together, please refer to OpenSees documentation and forums or see the zip file provided in the EXAMPLES section below.
 This element adds the capabilities of âImpactMaterialâ to âzeroLengthContact3D.â
 For simulating a surfacetosurface contact, the element can be defined for connecting the nodes on slave surface to the nodes on master surface.
 The element was found to be fastconverging and eliminating the need for extra elements and nodes in the modeling process.
See also
Truss ElementsÂ¶
Truss ElementÂ¶
This command is used to construct a truss element object. There are two ways to construct a truss element object:

element
('Truss', eleTag, *eleNodes, A, matTag, <'rho', rho>, <'cMass', cFlag>, <'doRayleigh', rFlag>) One way is to specify an area and a UniaxialMaterial identifier:

element
('TrussSection', eleTag, *eleNodes, A, secTag, <'rho', rho>, <'cMass', cFlag>, <'doRayleigh', rFlag>) the other is to specify a Section identifier:
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes A
(float)crosssectional area of element matTag
(int)tag associated with previouslydefined UniaxialMaterial secTag
(int)tag associated with previouslydefined Section rho
(float)mass per unit length, optional, default = 0.0 cFlag
(float)consistent mass flag, optional, default = 0
cFlag
= 0 lumped mass matrix (default)cFlag
= 1 consistent mass matrix
rFlag
(float)Rayleigh damping flag, optional, default = 0
rFlag
= 0 NO RAYLEIGH DAMPING (default)rFlag
= 1 include Rayleigh damping
Note
 The truss element DOES NOT include geometric nonlinearities, even when used with beamcolumns utilizing PDelta or Corotational transformations.
 When constructed with a UniaxialMaterial object, the truss element considers strainrate effects, and is thus suitable for use as a damping element.
 The valid queries to a truss element when creating an ElementRecorder object are âaxialForce,â âforces,â âlocalForceâ, deformations,â âmaterial matArg1 matArg2âŠ,â âsection sectArg1 sectArg2âŠâ There will be more queries after the interface for the methods involved have been developed further.
See also
Corotational Truss ElementÂ¶
This command is used to construct a corotational truss element object. There are two ways to construct a corotational truss element object:

element
('corotTruss', eleTag, *eleNodes, A, matTag, <'rho', rho>, <'cMass', cFlag>, <'doRayleigh', rFlag>) One way is to specify an area and a UniaxialMaterial identifier:

element
('corotTrussSection', eleTag, *eleNodes, secTag, <'rho', rho>, <'cMass', cFlag>, <'doRayleigh', rFlag>) the other is to specify a Section identifier:
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes A
(float)crosssectional area of element matTag
(int)tag associated with previouslydefined UniaxialMaterial secTag
(int)tag associated with previouslydefined Section rho
(float)mass per unit length, optional, default = 0.0 cFlag
(float)consistent mass flag, optional, default = 0
cFlag
= 0 lumped mass matrix (default)cFlag
= 1 consistent mass matrix
rFlag
(float)Rayleigh damping flag, optional, default = 0
rFlag
= 0 NO RAYLEIGH DAMPING (default)rFlag
= 1 include Rayleigh damping
Note
 When constructed with a UniaxialMaterial object, the corotational truss element considers strainrate effects, and is thus suitable for use as a damping element.
 The valid queries to a truss element when creating an ElementRecorder object are âaxialForce,â âstiff,â deformations,â âmaterial matArg1 matArg2âŠ,â âsection sectArg1 sectArg2âŠâ There will be more queries after the interface for the methods involved have been developed further.
 CorotTruss DOES NOT include Rayleigh damping by default.
See also
BeamColumn ElementsÂ¶
 Elastic Beam Column Element
 Elastic Beam Column Element with Stiffness Modifiers
 Elastic Timoshenko Beam Column Element
 Beam With Hinges Element
 dispBeamColumn
 forceBeamColumn
 nonlinearBeamColumn
 FlexureShear Interaction DisplacementBased BeamColumn Element
 MVLEM  MultipleVerticalLineElementModel for RC Walls
 SFI MVLEM  Cyclic ShearFlexure Interaction Model for RC Walls
Elastic Beam Column ElementÂ¶
This command is used to construct an elasticBeamColumn element object. The arguments for the construction of an elastic beamcolumn element depend on the dimension of the problem, (ndm)

element
('elasticBeamColumn', eleTag, *eleNodes, Area, E_mod, Iz, transfTag, <'mass', mass>, <'cMass'>, <'release', releaseCode>) For a twodimensional problem

element
('elasticBeamColumn', eleTag, *eleNodes, Area, E_mod, G_mod, Jxx, Iy, Iz, transfTag, <'mass', mass>, <'cMass'>) For a threedimensional problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes Area
(float)crosssectional area of element E_mod
(float)Youngâs Modulus G_mod
(float)Shear Modulus Jxx
(float)torsional moment of inertia of cross section Iz
(float)second moment of area about the local zaxis Iy
(float)second moment of area about the local yaxis transfTag
(int)identifier for previouslydefined coordinatetransformation (CrdTransf) object mass
(float)element mass per unit length (optional, default = 0.0) 'cMass'
(str)to form consistent mass matrix (optional, default = lumped mass matrix) 'releaseCode'
(int)moment release (optional, 2d only, 0=no release (default), 1=release at I, 2=release at J, 3=release at I and J)
See also
Elastic Beam Column Element with Stiffness ModifiersÂ¶
This command is used to construct a ModElasticBeam2d element object. The arguments for the construction of an elastic beamcolumn element with stiffness modifiers is applicable for 2D problems. This element should be used for modelling of a structural element with an equivalent combination of one elastic element with stiffnessproportional damping, and two springs at its two ends with no stiffness proportional damping to represent a prismatic section. The modelling technique is based on a number of analytical studies discussed in Zareian and Medina (2010) and Zareian and Krawinkler (2009) and is utilized in order to solve problems related to numerical damping in dynamic analysis of frame structures with concentrated plasticity springs.

element
('ModElasticBeam2d', eleTag, *eleNodes, Area, E_mod, Iz, K11, K33, K44, transfTag, <'mass', massDens>, <'cMass'>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes Area
(float)crosssectional area of element E_mod
(float)Youngâs Modulus Iz
(float)second moment of area about the local zaxis K11
(float)stiffness modifier for translation K33
(float)stiffness modifier for translation K44
(float)stiffness modifier for rotation transfTag
(int)identifier for previouslydefined coordinatetransformation (CrdTransf) object massDens
(float)element mass per unit length (optional, default = 0.0) 'cMass'
(str)to form consistent mass matrix (optional, default = lumped mass matrix)
See also
Elastic Timoshenko Beam Column ElementÂ¶
This command is used to construct an ElasticTimoshenkoBeam element object. A Timoshenko beam is a frame member that accounts for shear deformations. The arguments for the construction of an elastic Timoshenko beam element depend on the dimension of the problem, ndm:

element
('ElasticTimoshenkoBeam', eleTag, *eleNodes, E_mod, G_mod, Area, Iz, Avy, transfTag, <'mass', massDens>, <'cMass'>) For a twodimensional problem:

element
('ElasticTimoshenkoBeam', eleTag, *eleNodes, E_mod, G_mod, Area, Iz, Jxx, Iy, Iz, Avy, Avz, transfTag, <'mass', massDens>, <'cMass'>) For a threedimensional problem:
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes E_mod
(float)Youngâs Modulus G_mod
(float)Shear Modulus Area
(float)crosssectional area of element Jxx
(float)torsional moment of inertia of cross section Iy
(float)second moment of area about the local yaxis Iz
(float)second moment of area about the local zaxis Avy
(float)Shear area for the local yaxis Avz
(float)Shear area for the local zaxis transfTag
(int)identifier for previouslydefined coordinatetransformation (CrdTransf) object massDens
(float)element mass per unit length (optional, default = 0.0) 'cMass'
(str)to form consistent mass matrix (optional, default = lumped mass matrix)
See also
Beam With Hinges ElementÂ¶
This command is used to construct a forceBeamColumnElement element object, which is based on the noniterative (or iterative) flexibility formulation. The locations and weights of the element integration points are based on socalled plastic hinge integration, which allows the user to specify plastic hinge lenghts at the element ends. Twopoint Gauss integration is used on the element interior while twopoint GaussRadau integration is applied over lengths of 4LpI and 4LpJ at the element ends, viz. âmodified GaussRadau plastic hinge integrationâ. A total of six integration points are used in the element state determination (two for each hinge and two for the interior).
Users may be familiar with the beamWithHinges command format (see below); however, the format shown here allows for the simple but important case of using a material nonlinear section model on the element interior. The previous beamWithHinges command constrained the user to an elastic interior, which often led to unconservative estimates of the element resisting force when plasticity spread beyond the plastic hinge regions in to the element interior.
The advantages of this new format over the previous beamWithHinges command are
 Plasticity can spread beyond the plastic hinge regions
 Hinges can form on the element interior, e.g., due to distributed member loads
To create a beam element with hinges, one has to
use a forceBeamColumnElement element with following beamIntegration()
.
Note
'HingeRadau'
â twopoint GaussRadau applied to the hinge regions over 4LpI and 4LpJ (six element integration points)'HingeRadauTwo'
â twopoint GaussRadau in the hinge regions applied over LpI and LpJ (six element integration points)'HingeMidpoint'
â midpoint integration over the hinge regions (four element integration points)'HingeEndpoint'
â endpoint integration over the hinge regions (four element integration points)
See also
For more information on the behavior, advantages, and disadvantages of these approaches to plastic hinge integration, see
Scott, M.H. and G.L. Fenves. âPlastic Hinge Integration Methods for ForceBased BeamColumn Elementsâ, Journal of Structural Engineering, 132(2):244252, February 2006.
Scott, M.H. and K.L. Ryan. âMomentRotation Behavior of ForceBased Plastic Hinge Elementsâ, Earthquake Spectra, 29(2):597607, May 2013.
The primary advantages of HingeRadau are
 The user can specify a physically meaningful plastic hinge length
 The largest bending moment is captured at the element ends
 The exact numerical solution is recovered for a linearelastic prismatic beam
 The characteristic length is equal to the userspecified plastic hinge length when deformations localize at the element ends
while the primary disadvantages are
 The element postyield response is too flexible for strainhardening section response (consider using HingeRadauTwo)
 The user needs to know the plastic hinge length a priori (empirical equations are available)
dispBeamColumnÂ¶

element
('dispBeamColumn', eleTag, *eleNodes, transfTag, integrationTag, 'cMass', 'mass', mass=0.0) Create a dispBeamColumn element.
eleTag
(int)tag of the element eleNodes
(list (int))list of two node tags transfTag
(int)tag of transformation integrationTag
(int)tag of beamIntegration()
'cMass'
to form consistent mass matrix (optional, default = lumped mass matrix) mass
(float)element mass density (per unit length), from which a lumpedmass matrix is formed (optional)
forceBeamColumnÂ¶

element
('forceBeamColumn', eleTag, *eleNodes, transfTag, integrationTag, 'iter', maxIter=10, tol=1e12, 'mass', mass=0.0) Create a ForceBeamColumn element.
eleTag
(int)tag of the element eleNodes
(list (int))a list of two element nodes transfTag
(int)tag of transformation integrationTag
(int)tag of beamIntegration()
maxIter
(int)maximum number of iterations to undertake to satisfy element compatibility (optional) tol
(float)tolerance for satisfaction of element compatibility (optional) mass
(float)element mass density (per unit length), from which a lumpedmass matrix is formed (optional)
nonlinearBeamColumnÂ¶

element
('nonlinearBeamColumn', eleTag, *eleNodes, numIntgrPts, secTag, transfTag, 'iter', maxIter=10, tol=1e12, 'mass', mass=0.0, 'integration', intType) Create a nonlinearBeamColumn element. This element is for backward compatability.
eleTag
(int)tag of the element eleNodes
(list (int))a list of two element nodes numIntgrPts
(int)number of integration points. secTag
(int)tag of section transfTag
(int)tag of transformation maxIter
(int)maximum number of iterations to undertake to satisfy element compatibility (optional) tol
(float)tolerance for satisfaction of element compatibility (optional) mass
(float)element mass density (per unit length), from which a lumpedmass matrix is formed (optional) intType
(str)integration type (optional, default is
'Lobatto'
)'Lobatto'
'Legendre'
'Radau'
'NewtonCotes'
'Trapezoidal'
FlexureShear Interaction DisplacementBased BeamColumn ElementÂ¶
This command is used to construct a dispBeamColumnInt element object, which is a distributedplasticity, displacementbased beamcolumn element which includes interaction between flexural and shear components.

element
('dispBeamColumnInt', eleTag, *eleNodes, numIntgrPts, secTag, transfTag, cRot, <'mass', massDens>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes numIntgrPts
(int)number of integration points along the element. secTag
(int)identifier for previouslydefined section object transfTag
(int)identifier for previouslydefined coordinatetransformation (CrdTransf) object cRot
(float)identifier for element center of rotation (or center of curvature distribution). Fraction of the height distance from bottom to the center of rotation (0 to 1) massDens
(float)element mass density (per unit length), from which a lumpedmass matrix is formed (optional, default=0.0)
See also
MVLEM  MultipleVerticalLineElementModel for RC WallsÂ¶
The MVLEM element command is used to generate a twodimensional MultipleVerticalLineElementModel (MVLEM; Vulcano et al., 1988; Orakcal et al., 2004, Kolozvari et al., 2015) for simulation of flexuredominated RC wall behavior. A single model element incorporates six global degrees of freedom, three of each located at the center of rigid top and bottom beams, as illustrated in Figure 1a. The axial/flexural response of the MVLEM is simulated by a series of uniaxial elements (or macrofibers) connected to the rigid beams at the top and bottom (e.g., floor) levels, whereas the shear response is described by a shear spring located at height ch from the bottom of the wall element (Figure 1a). Shear and flexural responses of the model element are uncoupled. The relative rotation between top and bottom faces of the wall element occurs about the point located on the central axis of the element at height ch (Figure 1b). Rotations and resulting transverse displacements are calculated based on the wall curvature, derived from section and material properties, corresponding to the bending moment at height ch of each element (Figure 1b). A value of c=0.4 was recommended by Vulcano et al. (1988) based on comparison of the model response with experimental results.

element
('MVLEM', eleTag, Dens, *eleNodes, m, c, 'thick', *thick, 'width', *widths, 'rho', *rho, 'matConcrete', *matConcreteTags, 'matSteel', *matSteelTags, 'matShear', matShearTag) eleTag
(int)unique element object tag Dens
(float)Wall density eleNodes
(list (int))a list of two element nodes m
(int)Number of element macrofibers c
(float)Location of center of rotation from the iNode, c
= 0.4 (recommended)thick
(list (float))a list of m
macrofiber thicknesseswidths
(list (float))a list of m
macrofiber widthsrho
(list (float))a list of m reinforcing ratios corresponding to macrofibers; for each fiber: \(rho_i = A_{s,i}/A_{gross,i} (1 < i < m)\) matConcreteTags
(list (int))a list of m
uniaxialMaterial tags for concretematSteelTags
(list (int))a list of m
uniaxialMaterial tags for steelmatShearTag
(int)Tag of uniaxialMaterial for shear material
See also
SFI MVLEM  Cyclic ShearFlexure Interaction Model for RC WallsÂ¶
The SFI_MVLEM command is used to construct a ShearFlexure Interaction MultipleVerticalLineElement Model (SFIMVLEM, Kolozvari et al., 2015a, b, c), which captures interaction between axial/flexural and shear behavior of RC structural walls and columns under cyclic loading. The SFI_MVLEM element (Figure 1) incorporates 2D RC panel behavior described by the FixedStrutAngleModel (nDMaterial FSAM; Ulugtekin, 2010; Orakcal et al., 2012), into a 2D macroscopic fiberbased model (MVLEM). The interaction between axial and shear behavior is captured at each RC panel (macrofiber) level, which further incorporates interaction between shear and flexural behavior at the SFI_MVLEM element level.

element
('SFI_MVLEM', eleTag, *eleNodes, m, c, 'thick', *thick, 'width', *widths, 'mat', *mat_tags) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes m
(int)Number of element macrofibers c
(float)Location of center of rotation with from the iNode, c
= 0.4 (recommended)Thicknesses
(list (float))a list of m macrofiber thicknesses Widths
(list (float))a list of m macrofiber widths Material_tags
(list (int))a list of m macrofiber nDMaterial1 tags
See also
Joint ElementsÂ¶
BeamColumnJoint ElementÂ¶
This command is used to construct a twodimensional beamcolumnjoint element object. The element may be used with both twodimensional and threedimensional structures; however, load is transferred only in the plane of the element.

element
('beamColumnJoint', eleTag, *eleNodes, Mat1Tag, Mat2Tag, Mat3Tag, Mat4Tag, Mat5Tag, Mat6Tag, Mat7Tag, Mat8Tag, Mat9Tag, Mat10Tag, Mat11Tag, Mat12Tag, Mat13Tag, <eleHeightFac=1.0, eleWidthFac=1.0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes Mat1Tag
(int)uniaxial material tag for left barslip spring at node 1 Mat2Tag
(int)uniaxial material tag for right barslip spring at node 1 Mat3Tag
(int)uniaxial material tag for interfaceshear spring at node 1 Mat4Tag
(int)uniaxial material tag for lower barslip spring at node 2 Mat5Tag
(int)uniaxial material tag for upper barslip spring at node 2 Mat6Tag
(int)uniaxial material tag for interfaceshear spring at node 2 Mat7Tag
(int)uniaxial material tag for left barslip spring at node 3 Mat8Tag
(int)uniaxial material tag for right barslip spring at node 3 Mat9Tag
(int)uniaxial material tag for interfaceshear spring at node 3 Mat10Tag
(int)uniaxial material tag for lower barslip spring at node 4 Mat11Tag
(int)uniaxial material tag for upper barslip spring at node 4 Mat12Tag
(int)uniaxial material tag for interfaceshear spring at node 4 Mat13Tag
(int)uniaxial material tag for shearpanel eleHeightFac
(float)floating point value (as a ratio to the total height of the element) to be considered for determination of the distance in between the tensioncompression couples (optional, default: 1.0) eleWidthFac
(float)floating point value (as a ratio to the total width of the element) to be considered for determination of the distance in between the tensioncompression couples (optional, default: 1.0)
See also
ElasticTubularJoint ElementÂ¶
This command is used to construct an ElasticTubularJoint element object, which models joint flexibility of tubular joints in two dimensional analysis of any structure having tubular joints.

element
('ElasticTubularJoint', eleTag, *eleNodes, Brace_Diameter, Brace_Angle, E, Chord_Diameter, Chord_Thickness, Chord_Angle) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes Brace_Diameter
(float)outer diameter of brace Brace_Angle
(float)angle between brace and chord axis 0 < Brace_Angle < 90 E
(float)Youngâs Modulus Chord_Diameter
(float)outer diameter of chord Chord_Thickness
(float)thickness of chord Chord_Angle
(float)angle between chord axis and global xaxis 0 < Chord_Angle < 180
See also
Joint2D ElementÂ¶
This command is used to construct a twodimensional beamcolumnjoint element object. The two dimensional beamcolumn joint is idealized as a parallelogram shaped shear panel with adjacent elements connected to its midpoints. The midpoints of the parallelogram are referred to as external nodes. These nodes are the only analysis components that connect the joint element to the surrounding structure.

element
('Joint2D', eleTag, *eleNodes, <Mat1, Mat2, Mat3, Mat4>, MatC, LrgDspTag, <'damage', DmgTag>, <'damage', Dmg1 Dmg2 Dmg3 Dmg4 DmgC>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of five element nodes = [nd1,nd2,nd3,nd4,ndC]
.ndC
is the central node of beamcolumn joint. (the tagndC
is used to generate the internal node, thus, the node should not exist in the domain or be used by any other node)Mat1
(int)uniaxial material tag for interface rotational spring at node 1. Use a zero tag to indicate the case that a beamcolumn element is rigidly framed to the joint. (optional) Mat2
(int)uniaxial material tag for interface rotational spring at node 2. Use a zero tag to indicate the case that a beamcolumn element is rigidly framed to the joint. (optional) Mat3
(int)uniaxial material tag for interface rotational spring at node 3. Use a zero tag to indicate the case that a beamcolumn element is rigidly framed to the joint. (optional) Mat4
(int)uniaxial material tag for interface rotational spring at node 4. Use a zero tag to indicate the case that a beamcolumn element is rigidly framed to the joint. (optional) MatC
(int)uniaxial material tag for rotational spring of the central node that describes shear panel behavior LrgDspTag
(int)an integer indicating the flag for considering large deformations: * 0
 for small deformations and constant geometry *1
 for large deformations and time varying geometry *2
 for large deformations ,time varying geometry and length correctionDmgTag
(int)damage model tag Dmg1
(int)damage model tag for Mat1 Dmg2
(int)damage model tag for Mat2 Dmg3
(int)damage model tag for Mat3 Dmg4
(int)damage model tag for Mat4 DmgC
(int)panel damage model tag
See also
Link ElementsÂ¶
Two Node Link ElementÂ¶
This command is used to construct a twoNodeLink element object, which is defined by two nodes. The element can have zero or nonzero length. This element can have 1 to 6 degrees of freedom, where only the transverse and rotational degrees of freedom are coupled as long as the element has nonzero length. In addition, if the element length is larger than zero, the user can optionally specify how the PDelta moments around the local x and yaxis are distributed among a moment at node i, a moment at node j, and a shear couple. The sum of these three ratios is always equal to 1. In addition the shear center can be specified as a fraction of the element length from the iNode. The element does not contribute to the Rayleigh damping by default. If the element has nonzero length, the local xaxis is determined from the nodal geometry unless the optional xaxis vector is specified in which case the nodal geometry is ignored and the userdefined orientation is utilized. It is important to recognize that if this element has zero length, it does not consider the geometry as given by the nodal coordinates, but utilizes the userdefined orientation vectors to determine the directions of the springs.

element
('twoNodeLink', eleTag, *eleNodes, 'mat', *matTags, 'dir', *dir, <'orient', *vecx, *vecyp>, <'pDelta', *pDeltaVals>, <'shearDist', *shearDist>, <'doRayleigh'>, <'mass', m>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes matTags
(list (int))a list of tags associated with previouslydefined UniaxialMaterial objects dirs
(list (int))a list material directions:
 2Dcase:
1
,2
 translations along local x,y axes;3
 rotation about local z axis  3Dcase:
1
,2
,3
 translations along local x,y,z axes;4
,5
,6
 rotations about local x,y,z axes
vecx
(list (float))vector components in global coordinates defining local xaxis (optional) vecyp
(list (float))vector components in global coordinates defining local yaxis (optional) pDeltaVals
(list (float))PDelta moment contribution ratios, size of ratio vector is 2 for 2Dcase and 4 for 3Dcase (entries: [My_iNode, My_jNode, Mz_iNode, Mz_jNode]
)My_iNode
+My_jNode
<= 1.0,Mz_iNode
+Mz_jNode
<= 1.0. Remaining PDelta moments are resisted by shear couples. (optional)sDratios
(list (float))shear distances from iNode as a fraction of the element length, size of ratio vector is 1 for 2Dcase and 2 for 3Dcase. (entries: [dy_iNode, dz_iNode]
) (optional, default =[0.5, 0.5]
)'doRayleigh'
(str)to include Rayleigh damping from the element (optional, default = no Rayleigh damping contribution) m
(float)element mass (optional, default = 0.0)  2Dcase:
See also
Bearing ElementsÂ¶
 Elastomeric Bearing (Plasticity) Element
 Elastomeric Bearing (BoucWen) Element
 Flat Slider Bearing Element
 Single Friction Pendulum Bearing Element
 Triple Friction Pendulum Bearing Element
 Triple Friction Pendulum Element
 MultipleShearSpring Element
 KikuchiBearing Element
 YamamotoBiaxialHDR Element
 ElastomericX
 LeadRubberX
 HDR
 RJWatson EQS Bearing Element
 FPBearingPTV
Elastomeric Bearing (Plasticity) ElementÂ¶
This command is used to construct an elastomericBearing element object, which is defined by two nodes. The element can have zero length or the appropriate bearing height. The bearing has unidirectional (2D) or coupled (3D) plasticity properties for the shear deformations, and forcedeformation behaviors defined by UniaxialMaterials in the remaining two (2D) or four (3D) directions. By default (sDratio = 0.5) PDelta moments are equally distributed to the two endnodes. To avoid the introduction of artificial viscous damping in the isolation system (sometimes referred to as âdamping leakage in the isolation systemâ), the bearing element does not contribute to the Rayleigh damping by default. If the element has nonzero length, the local xaxis is determined from the nodal geometry unless the optional xaxis vector is specified in which case the nodal geometry is ignored and the userdefined orientation is utilized.

element
('elastomericBearingPlasticity', eleTag, *eleNodes, kInit, qd, alpha1, alpha2, mu, 'P', PMatTag, 'Mz', MzMatTag, <'orient', x1, x2, x3, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>) For a twodimensional problem

element
('elastomericBearingPlasticity', eleTag, *eleNodes, kInit, qd, alpha1, alpha2, mu, 'P', PMatTag, 'T', TMatTag, 'My', MyMatTag, 'Mz', MzMatTag, <'orient', <x1, x2, x3>, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>) For a threedimensional problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes kInit
(float)initial elastic stiffness in local shear direction qd
(float)characteristic strength alpha1
(float)post yield stiffness ratio of linear hardening component alpha2
(float)post yield stiffness ratio of nonlinear hardening component mu
(float)exponent of nonlinear hardening component PMatTag
(int)tag associated with previouslydefined UniaxialMaterial in axial direction TMatTag
(int)tag associated with previouslydefined UniaxialMaterial in torsional direction MyMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local yaxis MzMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local zaxis x1
x2
x3
(float)vector components in global coordinates defining local xaxis (optional) y1
y2
y3
(float)vector components in global coordinates defining local yaxis (optional) sDratio
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.5) 'doRayleigh'
(str)to include Rayleigh damping from the bearing (optional, default = no Rayleigh damping contribution) m
(float)element mass (optional, default = 0.0)
See also
Elastomeric Bearing (BoucWen) ElementÂ¶
This command is used to construct an elastomericBearing element object, which is defined by two nodes. The element can have zero length or the appropriate bearing height. The bearing has unidirectional (2D) or coupled (3D) plasticity properties for the shear deformations, and forcedeformation behaviors defined by UniaxialMaterials in the remaining two (2D) or four (3D) directions. By default (sDratio = 0.5) PDelta moments are equally distributed to the two endnodes. To avoid the introduction of artificial viscous damping in the isolation system (sometimes referred to as âdamping leakage in the isolation systemâ), the bearing element does not contribute to the Rayleigh damping by default. If the element has nonzero length, the local xaxis is determined from the nodal geometry unless the optional xaxis vector is specified in which case the nodal geometry is ignored and the userdefined orientation is utilized.

element
('ElastomericBearingBoucWen', eleTag, *eleNodes, kInit, qd, alpha1, alpha2, mu, eta, beta, gamma, 'P', PMatTag, 'Mz', MzMatTag, <'orient', *orientVals>, <'shearDist', shearDist>, <'doRayleigh'>, <'mass', mass>) For a twodimensional problem

element
('ElastomericBearingBoucWen', eleTag, *eleNodes, kInit, qd, alpha1, alpha2, mu, eta, beta, gamma, 'P', PMatTag, 'T', TMatTag, 'My', MyMatTag, 'Mz', MzMatTag, <'orient', *orientVals>, <'shearDist', shearDist>, <'doRayleigh'>, <'mass', mass>) For a threedimensional problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes kInit
(float)initial elastic stiffness in local shear direction qd
(float)characteristic strength alpha1
(float)post yield stiffness ratio of linear hardening component alpha2
(float)post yield stiffness ratio of nonlinear hardening component mu
(float)exponent of nonlinear hardening component eta
(float)yielding exponent (sharpness of hysteresis loop corners) (default = 1.0) beta
(float)first hysteretic shape parameter (default = 0.5) gamma
(float)second hysteretic shape parameter (default = 0.5) PMatTag
(int)tag associated with previouslydefined UniaxialMaterial in axial direction TMatTag
(int)tag associated with previouslydefined UniaxialMaterial in torsional direction MyMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local yaxis MzMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local zaxis orientVals
(list (int))vector components in global coordinates defining local xaxis (optional), vector components in global coordinates defining local yaxis (optional) shearDist
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.5) 'doRayleigh'
(str)to include Rayleigh damping from the bearing (optional, default = no Rayleigh damping contribution) mass
(float)element mass (optional, default = 0.0)
See also
Flat Slider Bearing ElementÂ¶
This command is used to construct a flatSliderBearing element object, which is defined by two nodes. The iNode represents the flat sliding surface and the jNode represents the slider. The element can have zero length or the appropriate bearing height. The bearing has unidirectional (2D) or coupled (3D) friction properties for the shear deformations, and forcedeformation behaviors defined by UniaxialMaterials in the remaining two (2D) or four (3D) directions. To capture the uplift behavior of the bearing, the userspecified UniaxialMaterial in the axial direction is modified for notension behavior. By default (sDratio = 0.0) PDelta moments are entirely transferred to the flat sliding surface (iNode). It is important to note that rotations of the flat sliding surface (rotations at the iNode) affect the shear behavior of the bearing. To avoid the introduction of artificial viscous damping in the isolation system (sometimes referred to as âdamping leakage in the isolation systemâ), the bearing element does not contribute to the Rayleigh damping by default. If the element has nonzero length, the local xaxis is determined from the nodal geometry unless the optional xaxis vector is specified in which case the nodal geometry is ignored and the userdefined orientation is utilized.

element
('flatSliderBearing', eleTag, *eleNodes, frnMdlTag, kInit, 'P', PMatTag, 'Mz', MzMatTag, <'orient', x1, x2, x3, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>, <'maxIter', iter, tol>) For a twodimensional problem

element
('flatSliderBearing', eleTag, *eleNodes, frnMdlTag, kInit, 'P', PMatTag, 'T', TMatTag, 'My', MyMatTag, 'Mz', MzMatTag, <'orient', <x1, x2, x3>, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>, <'iter', maxIter, tol>) For a threedimensional problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes frnMdlTag
(float)tag associated with previouslydefined FrictionModel kInit
(float)initial elastic stiffness in local shear direction PMatTag
(int)tag associated with previouslydefined UniaxialMaterial in axial direction TMatTag
(int)tag associated with previouslydefined UniaxialMaterial in torsional direction MyMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local yaxis MzMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local zaxis x1
x2
x3
(float)vector components in global coordinates defining local xaxis (optional) y1
y2
y3
(float)vector components in global coordinates defining local yaxis (optional) sDratio
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.0) 'doRayleigh'
(str)to include Rayleigh damping from the bearing (optional, default = no Rayleigh damping contribution) m
(float)element mass (optional, default = 0.0) iter
(int)maximum number of iterations to undertake to satisfy element equilibrium (optional, default = 20) tol
(float)convergence tolerance to satisfy element equilibrium (optional, default = 1E8)
See also
Single Friction Pendulum Bearing ElementÂ¶
This command is used to construct a singleFPBearing element object, which is defined by two nodes. The iNode represents the concave sliding surface and the jNode represents the articulated slider. The element can have zero length or the appropriate bearing height. The bearing has unidirectional (2D) or coupled (3D) friction properties (with postyield stiffening due to the concave sliding surface) for the shear deformations, and forcedeformation behaviors defined by UniaxialMaterials in the remaining two (2D) or four (3D) directions. To capture the uplift behavior of the bearing, the userspecified UniaxialMaterial in the axial direction is modified for notension behavior. By default (sDratio = 0.0) PDelta moments are entirely transferred to the concave sliding surface (iNode). It is important to note that rotations of the concave sliding surface (rotations at the iNode) affect the shear behavior of the bearing. To avoid the introduction of artificial viscous damping in the isolation system (sometimes referred to as âdamping leakage in the isolation systemâ), the bearing element does not contribute to the Rayleigh damping by default. If the element has nonzero length, the local xaxis is determined from the nodal geometry unless the optional xaxis vector is specified in which case the nodal geometry is ignored and the userdefined orientation is utilized.

element
('singleFPBearing', eleTag, *eleNodes, frnMdlTag, Reff, kInit, 'P', PMatTag, 'Mz', MzMatTag, <'orient', x1, x2, x3, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>, <'iter', maxIter, tol>) For a twodimensional problem

element
('singleFPBearing', eleTag, *eleNodes, frnMdlTag, Reff, kInit, 'P', PMatTag, 'T', TMatTag, 'My', MyMatTag, 'Mz', MzMatTag, <'orient', <x1, x2, x3>, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>, <'iter', maxIter, tol>) For a threedimensional problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes frnMdlTag
(float)tag associated with previouslydefined FrictionModel Reff
(float)effective radius of concave sliding surface kInit
(float)initial elastic stiffness in local shear direction PMatTag
(int)tag associated with previouslydefined UniaxialMaterial in axial direction TMatTag
(int)tag associated with previouslydefined UniaxialMaterial in torsional direction MyMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local y axis MzMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local zaxis x1
x2
x3
(float)vector components in global coordinates defining local xaxis (optional) y1
y2
y3
(float)vector components in global coordinates defining local yaxis (optional) sDratio
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.0) 'doRayleigh'
(str)to include Rayleigh damping from the bearing (optional, default = no Rayleigh damping contribution) m
(float)element mass (optional, default = 0.0) maxIter
(int)maximum number of iterations to undertake to satisfy element equilibrium (optional, default = 20) tol
(float)convergence tolerance to satisfy element equilibrium (optional, default = 1E8)
See also
Triple Friction Pendulum Bearing ElementÂ¶
This command is used to construct a Triple Friction Pendulum Bearing element object, which is defined by two nodes. The element can have zero length or the appropriate bearing height. The bearing has unidirectional (2D) or coupled (3D) friction properties (with postyield stiffening due to the concave sliding surface) for the shear deformations, and forcedeformation behaviors defined by UniaxialMaterials in the remaining two (2D) or four (3D) directions. To capture the uplift behavior of the bearing, the userspecified UniaxialMaterial in the axial direction is modified for notension behavior. PDelta moments are entirely transferred to the concave sliding surface (iNode). It is important to note that rotations of the concave sliding surface (rotations at the iNode) affect the shear behavior of the bearing. If the element has nonzero length, the local xaxis is determined from the nodal geometry unless the optional xaxis vector is specified in which case the nodal geometry is ignored and the userdefined orientation is utilized.

element
('TFP', eleTag, *eleNodes, R1, R2, R3, R4, Db1, Db2, Db3, Db4, d1, d2, d3, d4, mu1, mu2, mu3, mu4, h1, h2, h3, h4, H0, colLoad, <K>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes R1
(float)Radius of inner bottom sliding surface R2
(float)Radius of inner top sliding surface R3
(float)Radius of outer bottom sliding surface R4
(float)Radius of outer top sliding surface Db1
(float)Diameter of inner bottom sliding surface Db2
(float)Diameter of inner top sliding surface Db3
(float)Diameter of outer bottom sliding surface Db4
(float)Diameter of outer top sliding surface d1
(float)diameter of inner slider d2
(float)diameter of inner slider d3
(float)diameter of outer bottom slider d4
(float)diameter of outer top slider mu1
(float)friction coefficient of inner bottom sliding surface mu2
(float)friction coefficient of inner top sliding surface mu3
(float)friction coefficient of outer bottom sliding surface mu4
(float)friction coefficient of outer top sliding surface h1
(float)height from inner bottom sliding surface to center of bearing h2
(float)height from inner top sliding surface to center of bearing h3
(float)height from outer bottom sliding surface to center of bearing h4
(float)height from inner top sliding surface to center of bearing H0
(float)total height of bearing colLoad
(float)initial axial load on bearing (only used for first time step then load come from model) K
(float)optional, stiffness of spring in vertical dirn (dof 2 if ndm= 2, dof 3 if ndm = 3) (default=1.0e15)
See also
Triple Friction Pendulum ElementÂ¶

element
('TripleFrictionPendulum', eleTag, *eleNodes, frnTag1, frnTag2, frnTag3, vertMatTag, rotZMatTag, rotXMatTag, rotYMatTag, L1, L2, L3, d1, d2, d3, W, uy, kvt, minFv, tol) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes frnTag1
,frnTag2
frnTag3
(int)= tags associated with previouslydefined FrictionModels at the three sliding interfaces vertMatTag
(int)= Predefined material tag for COMPRESSION behavior of the bearing rotZMatTag
rotXMatTag
rotYMatTag
(int)= Predefined material tags for rotational behavior about 3axis, 1axis and 2axis, respectively. L1
L2
L3
(float)= effective radii. Li = R_i  h_i (see Figure 1) d1
d2
d3
(float)= displacement limits of pendulums (Figure 1). Displacement limit of the bearing is 2 d1
+d2
+d3
+L1
.d3
/L3
L1
.d2
/L2
W
(float)= axial force used for the first trial of the first analysis step. uy
(float)= lateral displacement where sliding of the bearing starts. Recommended value = 0.25 to 1 mm. A smaller value may cause convergence problem. kvt
(float)= Tension stiffness k_vt of the bearing. minFv (>=0)
(float)= minimum vertical compression force in the bearing used for computing the horizontal tangent stiffness matrix from the normalized tangent stiffness matrix of the element. minFv
is substituted for the actual compressive force when it is less thanminFv
, and prevents the element from using a negative stiffness matrix in the horizontal direction when uplift occurs. The vertical nodal force returned to nodes is always computed fromkvc
(orkvt
) and vertical deformation, and thus is not affected byminFv
.tol
(float)= relative tolerance for checking the convergence of the element. Recommended value = 1.e10 to 1.e3.
See also
MultipleShearSpring ElementÂ¶
This command is used to construct a multipleShearSpring (MSS) element object, which is defined by two nodes. This element consists of a series of identical shear springs arranged radially to represent the isotropic behavior in the local yz plane.

element
('multipleShearSpring', eleTag, *eleNodes, nSpring, 'mat', matTag, <'lim', lim>, <'orient', <x1, x2, x3>, yp1, yp2, yp3>, <'mass', mass>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes nSpring
(int)number of springs matTag
(int)tag associated with previouslydefined UniaxialMaterial object lim
(float)minimum deformation to calculate equivalent coefficient (see note 1) x1
x2
x3
(float)vector components in global coordinates defining local xaxis yp1
yp2
yp3
(float)vector components in global coordinates defining vector yp which lies in the local xy plane for the element mass
(float)element mass
Note
If dsp
is positive and the shear deformation of MSS exceeds dsp
, this element calculates equivalent coefficient to adjust force and stiffness of MSS. The adjusted MSS force and stiffness reproduce the behavior of the previously defined uniaxial material under monotonic loading in every direction. If dsp
is zero, the element does not calculate the equivalent coefficient.
See also
KikuchiBearing ElementÂ¶
This command is used to construct a KikuchiBearing element object, which is defined by two nodes. This element consists of multiple shear spring model (MSS) and multiple normal spring model (MNS).

element
('KikuchiBearing', eleTag, *eleNodes, 'shape', shape, 'size', size, totalRubber, <'totalHeight', totalHeight>, 'nMSS', nMSS, 'matMSS', matMSSTag, <'limDisp', limDisp>, 'nMNS', nMNS, 'matMNS', matMNSTag, <'lambda', lambda>, <'orient', <x1, x2, x3>, yp1, yp2, yp3>, <'mass', m>, <'noPDInput'>, <'noTilt'>, <'adjustPDOutput', ci, cj>, <'doBalance', limFo, limFi, nIter>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes shape
(float)following shapes are available: round, square size
(float)diameter (round shape), length of edge (square shape) totalRubber
(float)total rubber thickness totalHeight
(float)total height of the bearing (defaulut: distance between iNode and jNode) nMSS
(int)number of springs in MSS = nMSS matMSSTag
(int)matTag for MSS limDisp
(float)minimum deformation to calculate equivalent coefficient of MSS (see note 1) nMNS
(int)number of springs in MNS = nMNS*nMNS (for round and square shape) matMNSTag
(int)matTag for MNS lambda
(float)parameter to calculate compression modulus distribution on MNS (see note 2) x1
x2
x3
(float)vector components in global coordinates defining local xaxis yp1
yp2
yp3
(float)vector components in global coordinates defining vector yp which lies in the local xy plane for the element m
(float)element mass 'noPDInput'
(str)not consider PDelta moment 'noTilt'
(str)not consider tilt of rigid link ci
cj
(float)PDelta moment adjustment for reaction force (default: ci
=0.5,cj
=0.5)limFo
limFi
nIter
(float)tolerance of external unbalanced force ( limFo
), tolorance of internal unbalanced force (limFi
), number of iterations to get rid of internal unbalanced force (nIter
)
See also
YamamotoBiaxialHDR ElementÂ¶
This command is used to construct a YamamotoBiaxialHDR element object, which is defined by two nodes. This element can be used to represent the isotropic behavior of highdamping rubber bearing in the local yz plane.

element
('YamamotoBiaxialHDR', eleTag, *eleNodes, Tp, DDo, DDi, Hr, <'coRS`, cr, cs>, <'orient`, *vecx, *vecyp>, <'mass`, m>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes Tp
(int)compound type = 1 : X0.6R manufactured by Bridgestone corporation. DDo
(float)outer diameter [m] DDi
(float)bore diameter [m] Hr
(float)total thickness of rubber layer [m] Optional Data cr
cs
(float)coefficients for shear stress components of tau_r and tau_s vecx
(list (float))a list of vector components in global coordinates defining local xaxis (optional) vecyp
(list (float))a list of vector components in global coordinates defining vector yp which lies in the local xy plane for the element. m
(float)element mass [kg]
See also
ElastomericXÂ¶
This command is used to construct an ElastomericX bearing element object in threedimension. The 3D continuum geometry of an elastomeric bearing is modeled as a 2node, 12 DOF discrete element. This elements extends the formulation of Elastomeric_Bearing_(BoucWen)_Element element. However, instead of the user providing material models as input arguments, it only requires geometric and material properties of an elastomeric bearing as arguments. The material models in six direction are formulated within the element from input arguments. The timedependent values of mechanical properties (e.g., shear stiffness, buckling load capacity) can also be recorded using the âparametersâ recorder.

element
('ElastomericX', eleTag, *eleNodes, Fy, alpha, Gr, Kbulk, D1, D2, ts, tr, n, <<x1, x2, x3>, y1, y2, y3>, <kc>, <PhiM>, <ac>, <sDratio>, <m>, <cd>, <tc>, <tag1>, <tag2>, <tag3>, <tag4>) For 3D problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes Fy
(float)yield strength alpha
(float)postyield stiffness ratio Gr
(float)shear modulus of elastomeric bearing Kbulk
(float)bulk modulus of rubber D1
(float)internal diameter D2
(float)outer diameter (excluding cover thickness) ts
(float)single steel shim layer thickness tr
(float)single rubber layer thickness n
(int)number of rubber layers x1
x2
x3
(float)vector components in global coordinates defining local xaxis (optional) y1
y2
y3
(float)vector components in global coordinates defining local yaxis (optional) kc
(float)cavitation parameter (optional, default = 10.0) PhiM
(float)damage parameter (optional, default = 0.5) ac
(float)strength reduction parameter (optional, default = 1.0) sDratio
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.5) m
(float)element mass (optional, default = 0.0) cd
(float)viscous damping parameter (optional, default = 0.0) tc
(float)cover thickness (optional, default = 0.0) tag1
(float)Tag to include cavitation and postcavitation (optional, default = 0) tag2
(float)Tag to include buckling load variation (optional, default = 0) tag3
(float)Tag to include horizontal stiffness variation (optional, default = 0) tag4
(float)Tag to include vertical stiffness variation (optional, default = 0)
Note
Because default values of heating parameters are in SI units, user must override the default heating parameters values if using Imperial units
User should distinguish between yield strength of elastomeric bearing (\(F_y\)) and characteristic strength (\(Q_d\)): \(Q_d=F_y*(1alpha)\)
See also
LeadRubberXÂ¶
This command is used to construct a LeadRubberX bearing element object in threedimension. The 3D continuum geometry of a lead rubber bearing is modeled as a 2node, 12 DOF discrete element. It extends the formulation of ElastomericX by including strength degradation in lead rubber bearing due to heating of the leadcore. The LeadRubberX element requires only the geometric and material properties of an elastomeric bearing as arguments. The material models in six direction are formulated within the element from input arguments. The timedependent values of mechanical properties (e.g., shear stiffness, buckling load capacity, temperature in the leadcore, yield strength) can also be recorded using the âparametersâ recorder.

element
('LeadRubberX', eleTag, *eleNodes, Fy, alpha, Gr, Kbulk, D1, D2, ts, tr, n, <<x1, x2, x3>, y1, y2, y3>, <kc>, <PhiM>, <ac>, <sDratio>, <m>, <cd>, <tc>, <qL>, <cL>, <kS>, <aS>, <tag1>, <tag2>, <tag3>, <tag4>, <tag5>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes Fy
(float)yield strength alpha
(float)postyield stiffness ratio Gr
(float)shear modulus of elastomeric bearing Kbulk
(float)bulk modulus of rubber D1
(float)internal diameter D2
(float)outer diameter (excluding cover thickness) ts
(float)single steel shim layer thickness tr
(float)single rubber layer thickness n
(int)number of rubber layers x1
x2
x3
(float)vector components in global coordinates defining local xaxis (optional) y1
y2
y3
(float)vector components in global coordinates defining local yaxis (optional) kc
(float)cavitation parameter (optional, default = 10.0) PhiM
(float)damage parameter (optional, default = 0.5) ac
(float)strength reduction parameter (optional, default = 1.0) sDratio
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.5) m
(float)element mass (optional, default = 0.0) cd
(float)viscous damping parameter (optional, default = 0.0) tc
(float)cover thickness (optional, default = 0.0) qL
(float)density of lead (optional, default = 11200 kg/m3) cL
(float)specific heat of lead (optional, default = 130 Nm/kg oC) kS
(float)thermal conductivity of steel (optional, default = 50 W/m oC) aS
(float)thermal diffusivity of steel (optional, default = 1.41e05 m2/s) tag1
(int)Tag to include cavitation and postcavitation (optional, default = 0) tag2
(int)Tag to include buckling load variation (optional, default = 0) tag3
(int)Tag to include horizontal stiffness variation (optional, default = 0) tag4
(int)Tag to include vertical stiffness variation (optional, default = 0) tag5
(int)Tag to include strength degradation in shear due to heating of lead core (optional, default = 0)
Note
Because default values of heating parameters are in SI units, user must override the default heating parameters values if using Imperial units
User should distinguish between yield strength of elastomeric bearing (\(F_y\)) and characteristic strength (\(Q_d\)): \(Q_d=F_y*(1alpha)\)
See also
HDRÂ¶
This command is used to construct an HDR bearing element object in threedimension. The 3D continuum geometry of an high damping rubber bearing is modeled as a 2node, 12 DOF discrete element. This is the third element in the series of elements developed for analysis of baseisolated structures under extreme loading (others being ElastomericX and LeadRubberX). The major difference between HDR element with ElastomericX is the hysteresis model in shear. The HDR element uses a model proposed by Grant et al. (2004) to capture the shear behavior of a high damping rubber bearing. The timedependent values of mechanical properties (e.g., vertical stiffness, buckling load capacity) can also be recorded using the âparametersâ recorder.

element
('HDR', eleTag, *eleNodes, Gr, Kbulk, D1, D2, ts, tr, n, a1, a2, a3, b1, b2, b3, c1, c2, c3, c4, <<x1, x2, x3>, y1, y2, y3>, <kc>, <PhiM>, <ac>, <sDratio>, <m>, <tc>) For 3D problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes Gr
(float)shear modulus of elastomeric bearing Kbulk
(float)bulk modulus of rubber D1
(float)internal diameter D2
(float)outer diameter (excluding cover thickness) ts
(float)single steel shim layer thickness tr
(float)single rubber layer thickness n
(int)number of rubber layers a1
a2
a3
b1
b2
b3
c1
c2
c3
c4
(float)parameters of the Grant model x1
x2
x3
(float)vector components in global coordinates defining local xaxis (optional) y1
y2
y3
(float)vector components in global coordinates defining local yaxis (optional) kc
(float)cavitation parameter (optional, default = 10.0) PhiM
(float)damage parameter (optional, default = 0.5) ac
(float)strength reduction parameter (optional, default = 1.0) sDratio
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.5) m
(float)element mass (optional, default = 0.0) tc
(float)cover thickness (optional, default = 0.0)
See also
RJWatson EQS Bearing ElementÂ¶
This command is used to construct a RJWatsonEqsBearing element object, which is defined by two nodes. The iNode represents the masonry plate and the jNode represents the sliding surface plate. The element can have zero length or the appropriate bearing height. The bearing has unidirectional (2D) or coupled (3D) friction properties (with postyield stiffening due to the massenergyregulator (MER) springs) for the shear deformations, and forcedeformation behaviors defined by UniaxialMaterials in the remaining two (2D) or four (3D) directions. To capture the uplift behavior of the bearing, the userspecified UniaxialMaterial in the axial direction is modified for notension behavior. By default (sDratio = 1.0) PDelta moments are entirely transferred to the sliding surface (jNode). It is important to note that rotations of the sliding surface (rotations at the jNode) affect the shear behavior of the bearing. To avoid the introduction of artificial viscous damping in the isolation system (sometimes referred to as âdamping leakage in the isolation systemâ), the bearing element does not contribute to the Rayleigh damping by default. If the element has nonzero length, the local xaxis is determined from the nodal geometry unless the optional xaxis vector is specified in which case the nodal geometry is ignored and the userdefined orientation is utilized.

element
('RJWatsonEqsBearing', eleTag, *eleNodes, frnMdlTag, kInit, 'P', PMatTag, 'Vy', VyMatTag, 'Mz', MzMatTag, <'orient', x1, x2, x3, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>, <'iter', maxIter, tol>) For a twodimensional problem

element
('RJWatsonEqsBearing', eleTag, *eleNodes, frnMdlTag, kInit, 'P', PMatTag, 'Vy', VyMatTag, 'Vz', VzMatTag, 'T', TMatTag, 'My', MyMatTag, 'Mz', MzMatTag, <'orient', <x1, x2, x3>, y1, y2, y3>, <'shearDist', sDratio>, <'doRayleigh'>, <'mass', m>, <'iter', maxIter, tol>) For a threedimensional problem
eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes frnMdlTag
(float)tag associated with previouslydefined FrictionModel kInit
(float)initial stiffness of sliding friction component in local shear direction 'P'
PMatTag
(int)tag associated with previouslydefined UniaxialMaterial in axial direction 'Vy'
VyMatTag
(int)tag associated with previouslydefined UniaxialMaterial in shear direction along local yaxis (MER spring behavior not including friction) 'Vz'
VzMatTag
(int)tag associated with previouslydefined UniaxialMaterial in shear direction along local zaxis (MER spring behavior not including friction) 'T'
TMatTag
(int)tag associated with previouslydefined UniaxialMaterial in torsional direction 'My'
MyMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local yaxis 'Mz'
MzMatTag
(int)tag associated with previouslydefined UniaxialMaterial in moment direction around local zaxis x1
x2
x3
(float)vector components in global coordinates defining local xaxis (optional) y1
y2
y3
(float)vector components in global coordinates defining local yaxis (optional) sDratio
(float)shear distance from iNode as a fraction of the element length (optional, default = 0.0) 'doRayleigh'
(str)to include Rayleigh damping from the bearing (optional, default = no Rayleigh damping contribution) m
(float)element mass (optional, default = 0.0) maxIter
(int)maximum number of iterations to undertake to satisfy element equilibrium (optional, default = 20) tol
(float)convergence tolerance to satisfy element equilibrium (optional, default = 1E8)
See also
FPBearingPTVÂ¶
The FPBearingPTV command creates a single Friction Pendulum bearing element, which is capable of accounting for the changes in the coefficient of friction at the sliding surface with instantaneous values of the sliding velocity, axial pressure and temperature at the sliding surface. The constitutive modelling is similar to the existing singleFPBearing element, otherwise. The FPBearingPTV element has been verified and validated in accordance with the ASME guidelines, details of which are presented in Chapter 4 of Kumar et al. (2015a).

element
('FPBearingPTV', eleTag, *eleNodes, MuRef, IsPressureDependent, pRef, IsTemperatureDependent, Diffusivity, Conductivity, IsVelocityDependent, rateParameter, ReffectiveFP, Radius_Contact, kInitial, theMaterialA, theMaterialB, theMaterialC, theMaterialD, x1, x2, x3, y1, y2, y3, shearDist, doRayleigh, mass, iter, tol, unit) eleTag
(int)unique element object tag eleNodes
(list (int))a list of two element nodes MuRef
(float)Reference coefficient of friction IsPressureDependent
(int)1 if the coefficient of friction is a function of instantaneous axial pressure pRef
(float)Reference axial pressure (the bearing pressure under static loads) IsTemperatureDependent
(int)1 if the coefficient of friction is a function of instantaneous temperature at the sliding surface Diffusivity
(float)Thermal diffusivity of steel Conductivity
(float)Thermal conductivity of steel IsVelocityDependent
(int)1 if the coefficient of friction is a function of instantaneous velocity at the sliding surface rateParameter
(float)The exponent that determines the shape of the coefficient of friction vs. sliding velocity curve ReffectiveFP
(float)Effective radius of curvature of the sliding surface of the FPbearing Radius_Contact
(float)Radius of contact area at the sliding surface kInitial
(float)Lateral stiffness of the sliding bearing before sliding begins theMaterialA
(int)Tag for the uniaxial material in the axial direction theMaterialB
(int)Tag for the uniaxial material in the torsional direction theMaterialC
(int)Tag for the uniaxial material for rocking about local Y axis theMaterialD
(int)Tag for the uniaxial material for rocking about local Z axis x1
x2
x3
(float)Vector components to define local X axis y1
y2
y3
(float)Vector components to define local Y axis shearDist
(float)Shear distance from iNode as a fraction of the length of the element doRayleigh
(int)To include Rayleigh damping from the bearing mass
(float)Element mass iter
(int)Maximum number of iterations to satisfy the equilibrium of element tol
(float)Convergence tolerance to satisfy the equilibrium of the element unit
(int)Tag to identify the unit from the list below.
1
: N, m, s, C2
: kN, m, s, C3
: N, mm, s, C4
: kN, mm, s, C5
: lb, in, s, C6
: kip, in, s, C7
: lb, ft, s, C8
: kip, ft, s, C
See also
Quadrilateral ElementsÂ¶
 Quad Element
 Shell Element
 ShellDKGQ
 ShellDKGT
 ShellNLDKGQ
 ShellNLDKGT
 ShellNL
 Bbar Plane Strain Quadrilateral Element
 Enhanced Strain Quadrilateral Element
 SSPquad Element
Quad ElementÂ¶
This command is used to construct a FourNodeQuad element object which uses a bilinear isoparametric formulation.

element
('quad', eleTag, *eleNodes, thick, type, matTag, <pressure=0.0, rho=0.0, b1=0.0, b2=0.0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order thick
(float)element thickness type
(str)string representing material behavior. The type parameter can be either 'PlaneStrain'
or'PlaneStress'
matTag
(int)tag of nDMaterial pressure
(float)surface pressure (optional, default = 0.0) rho
(float)element mass density (per unit volume) from which a lumped element mass matrix is computed (optional, default=0.0) b1
b2
(float)constant body forces defined in the isoparametric domain (optional, default=0.0)
Note
 Consistent nodal loads are computed from the pressure and body forces.
 The valid queries to a Quad element when creating an ElementRecorder object are âforcesâ, âstresses,â and âmaterial $matNum matArg1 matArg2 âŠâ Where $matNum refers to the material object at the integration point corresponding to the node numbers in the isoparametric domain.
See also
Shell ElementÂ¶
This command is used to construct a ShellMITC4 element object, which uses a bilinear isoparametric formulation in combination with a modified shear interpolation to improve thinplate bending performance.

element
('ShellMITC4', eleTag, *eleNodes, secTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order secTag
(int)tag associated with previouslydefined SectionForceDeformation object. Currently must be either a 'PlateFiberSection'
, or'ElasticMembranePlateSection'
Note
 The valid queries to a Quad element when creating an ElementRecorder object are âforcesâ, âstresses,â and âmaterial $matNum matArg1 matArg2 âŠâ Where $matNum refers to the material object at the integration point corresponding to the node numbers in the isoparametric domain.
 It is a 3D element with 6 dofs and CAN NOT be used in 2D domain.
See also
ShellDKGQÂ¶
This command is used to construct a ShellDKGQ element object, which is a quadrilateral shell element based on the theory of generalized conforming element.

element
('ShellDKGQ', eleTag, *eleNodes, secTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order secTag
(int)tag associated with previouslydefined SectionForceDeformation object. Currently can be a 'PlateFiberSection'
, a'ElasticMembranePlateSection'
and a'LayeredShell'
section
See also
ShellDKGTÂ¶
This command is used to construct a ShellDKGT element object, which is a triangular shell element based on the theory of generalized conforming element.

element
('ShellDKGT', eleTag, *eleNodes, secTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of three element nodes in clockwise or counterclockwise order secTag
(int)tag associated with previouslydefined SectionForceDeformation object. currently can be a 'PlateFiberSection'
, a'ElasticMembranePlateSection'
and a'LayeredShell'
section
See also
ShellNLDKGQÂ¶
This command is used to construct a ShellNLDKGQ element object accounting for the geometric nonlinearity of large deformation using the updated Lagrangian formula, which is developed based on the ShellDKGQ element.

element
('ShellNLDKGQ', eleTag, *eleNodes, secTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order secTag
(int)tag associated with previouslydefined SectionForceDeformation object. currently can be a 'PlateFiberSection'
, a'ElasticMembranePlateSection'
and a'LayeredShell'
section
See also
ShellNLDKGTÂ¶
This command is used to construct a ShellNLDKGT element object accounting for the geometric nonlinearity of large deformation using the updated Lagrangian formula, which is developed based on the ShellDKGT element.

element
('ShellNLDKGT', eleTag, *eleNodes, secTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of three element nodes in clockwise or counterclockwise order around the element secTag
(int)tag associated with previouslydefined SectionForceDeformation object. currently can be a 'PlateFiberSection'
, a'ElasticMembranePlateSection'
and a'LayeredShell'
section
See also
ShellNLÂ¶

element
('ShellNL', eleTag, *eleNodes, secTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of nine element nodes, input is the typical, firstly four corner nodes counterclockwise, then midside nodes counterclockwise and finally the central node secTag
(int)tag associated with previouslydefined SectionForceDeformation object. currently can be a 'PlateFiberSection'
, a'ElasticMembranePlateSection'
and a'LayeredShell'
section
See also
Bbar Plane Strain Quadrilateral ElementÂ¶
This command is used to construct a fournode quadrilateral element object, which uses a bilinear isoparametric formulation along with a mixed volume/pressure Bbar assumption. This element is for plane strain problems only.

element
('bbarQuad', eleTag, *eleNodes, thick, matTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order thick
(float)element thickness matTag
(int)tag of nDMaterial
Note
 PlainStrain only.
 The valid queries to a Quad element when creating an ElementRecorder object are âforcesâ, âstresses,â and âmaterial $matNum matArg1 matArg2 âŠâ Where $matNum refers to the material object at the integration point corresponding to the node numbers in the isoparametric domain.
See also
Enhanced Strain Quadrilateral ElementÂ¶
This command is used to construct a fournode quadrilateral element, which uses a bilinear isoparametric formulation with enhanced strain modes.

element
('enhancedQuad', eleTag, *eleNodes, thick, type, matTag) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order thick
(float)element thickness type
(str)string representing material behavior. Valid options depend on the NDMaterial object and its available material formulations. The type parameter can be either 'PlaneStrain'
or'PlaneStress'
matTag
(int)tag of nDMaterial
See also
SSPquad ElementÂ¶
This command is used to construct a SSPquad element object.

element
('SSPquad', eleTag, *eleNodes, matTag, type, thick, <b1, b2>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order thick
(float)thickness of the element in outofplane direction type
(str)string to relay material behavior to the element, can be either 'PlaneStrain'
or'PlaneStress'
matTag
(int)unique integer tag associated with previouslydefined nDMaterial object b1
b2
(float)constant body forces in global x and ydirections, respectively (optional, default = 0.0) The SSPquad element is a fournode quadrilateral element using physically stabilized singlepoint integration (SSP â> Stabilized Single Point). The stabilization incorporates an assumed strain field in which the volumetric dilation and the shear strain associated with the the hourglass modes are zero, resulting in an element which is free from volumetric and shear locking. The elimination of shear locking results in greater coarse mesh accuracy in bending dominated problems, and the elimination of volumetric locking improves accuracy in nearlyincompressible problems. Analysis times are generally faster than corresponding full integration elements. The formulation for this element is identical to the solid phase portion of the SSPquadUP element as described by McGann et al. (2012).
Note
 Valid queries to the SSPquad element when creating an ElementalRecorder object correspond to those for the nDMaterial object assigned to the element (e.g., âstressâ, âstrainâ). Material response is recorded at the single integration point located in the center of the element.
 The SSPquad element was designed with intentions of duplicating the functionality of the Quad Element. If an example is found where the SSPquad element cannot do something that works for the Quad Element, e.g., material updating, please contact the developers listed below so the bug can be fixed.
See also
Triangular ElementsÂ¶
Tri31 ElementÂ¶
This command is used to construct a constant strain triangular element (Tri31) which uses three nodes and one integration points.

element
('Tri31', eleTag, *eleNodes, thick, type, matTag, <pressure, rho, b1, b2>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of three element nodes in counterclockwise order thick
(float)element thickness type
(str)string representing material behavior. The type parameter can be either 'PlaneStrain'
or'PlaneStress'
matTag
(int)tag of nDMaterial pressure
(float)surface pressure (optional, default = 0.0) rho
(float)element mass density (per unit volume) from which a lumped element mass matrix is computed (optional, default=0.0) b1
b2
(float)constant body forces defined in the domain (optional, default=0.0)
Note
 Consistent nodal loads are computed from the pressure and body forces.
 The valid queries to a Tri31 element when creating an ElementRecorder object are âforcesâ, âstresses,â and âmaterial $matNum matArg1 matArg2 âŠâ Where $matNum refers to the material object at the integration point corresponding to the node numbers in the domain.
See also
Brick ElementsÂ¶
Standard Brick ElementÂ¶
This element is used to construct an eightnode brick element object, which uses a trilinear isoparametric formulation.

element
('stdBrick', eleTag, *eleNodes, matTag, <b1, b2, b3>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of eight element nodes in bottom and top faces and in counterclockwise order matTag
(int)tag of nDMaterial b1
b2
b3
(float)body forces in global x,y,z directions
Note
 The valid queries to a Brick element when creating an ElementRecorder object are âforcesâ, âstresses,â (âstrainsâ version > 2.2.0) and âmaterial $matNum matArg1 matArg2 âŠâ Where $matNum refers to the material object at the integration point corresponding to the node numbers in the isoparametric domain.
 This element can only be defined in ndm 3 ndf 3
See also
Bbar Brick ElementÂ¶
This command is used to construct an eightnode mixed volume/pressure brick element object, which uses a trilinear isoparametric formulation.

element
('bbarBrick', eleTag, *eleNodes, matTag, <b1, b2, b3>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of eight element nodes in bottom and top faces and in counterclockwise order matTag
(int)tag of nDMaterial b1
b2
b3
(float)body forces in global x,y,z directions
Note
 Node numbering for this element is different from that for the eightnode brick (Brick8N) element.
 The valid queries to a Quad element when creating an ElementRecorder object are âforcesâ, âstressesâ, âstrainsâ, and âmaterial $matNum matArg1 matArg2 âŠâ Where $matNum refers to the material object at the integration point corresponding to the node numbers in the isoparametric domain.
See also
Twenty Node Brick ElementÂ¶
The element is used to construct a twentynode three dimensional element object

element
('20NodeBrick', eleTag, *eleNodes, matTag, bf1, bf2, bf3, massDen) eleTag
(int)unique element object tag eleNodes
(list (int))a list of twenty element nodes, input order is shown in notes below matTag
(int)material tag associated with previsoulydefined NDMaterial object bf1
bf2
bf3
(float)body force in the direction of global coordinates x, y and z massDen
(float)mass density (mass/volume)
Note
The valid queries to a 20NodeBrick element when creating an ElementRecorder object are âforce,â âstiffness,â stressâ, âgausspointâ or âplasticâ. The output is given as follows:
âstressâ
the six stress components from each Gauss points are output by the order: sigma_xx, sigma_yy, sigma_zz, sigma_xy, sigma_xz,sigma_yz
âgausspointâ
the coordinates of all Gauss points are printed out
âplasticâ
the equivalent deviatoric plastic strain from each Gauss point is output in the same order as the coordinates are printed
See also
SSPbrick ElementÂ¶
This command is used to construct a SSPbrick element object.

element
('SSPbrick', eleTag, *eleNodes, matTag, <b1, b2, b3>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of eight element nodes in bottom and top faces and in counterclockwise order matTag
(int)unique integer tag associated with previouslydefined nDMaterial object b1
b2
b3
(float)constant body forces in global x, y, and zdirections, respectively (optional, default = 0.0)
The SSPbrick element is an eightnode hexahedral element using physically stabilized singlepoint integration (SSP â> Stabilized Single Point). The stabilization incorporates an enhanced assumed strain field, resulting in an element which is free from volumetric and shear locking. The elimination of shear locking results in greater coarse mesh accuracy in bending dominated problems, and the elimination of volumetric locking improves accuracy in nearlyincompressible problems. Analysis times are generally faster than corresponding full integration elements.
Note
 Valid queries to the SSPbrick element when creating an ElementalRecorder object correspond to those for the nDMaterial object assigned to the element (e.g., âstressâ, âstrainâ). Material response is recorded at the single integration point located in the center of the element.
 The SSPbrick element was designed with intentions of duplicating the functionality of the stdBrick Element. If an example is found where the SSPbrick element cannot do something that works for the stdBrick Element, e.g., material updating, please contact the developers listed below so the bug can be fixed.
See also
Tetrahedron ElementsÂ¶
FourNodeTetrahedronÂ¶
This command is used to construct a standard fournode tetrahedron element objec with onepoint Gauss integration.

element
('FourNodeTetrahedron', eleTag, *eleNodes, matTag, <b1, b2, b3>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes matTag
(int)tag of nDMaterial b1
b2
b3
(float)body forces in global x,y,z directions
See also
UC San Diego up element (saturated soil)Â¶
 Four Node Quad up Element
 Brick up Element
 BbarQuad up Element
 BbarBrick up Element
 Nine Four Node Quad up Element
 Twenty Eight Node Brick up Element
Four Node Quad up ElementÂ¶
FourNodeQuadUP is a fournode planestrain element using bilinear isoparametric formulation. This element is implemented for simulating dynamic response of solidfluid fully coupled material, based on Biotâs theory of porous medium. Each element node has 3 degreesoffreedom (DOF): DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p).

element
('quadUP', eleTag, *eleNodes, thick, matTag, bulk, fmass, hPerm, vPerm, <b1=0, b2=0, t=0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order thick
(float)Element thickness matTag
(int)Tag of an NDMaterial object (previously defined) of which the element is composed bulk
(float)Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: \(B_c \approx B_f/n\)
where \(B_f\) is the bulk modulus of fluid phase (\(2.2\times 10^6\) kPa (or \(3.191\times 10^5\) psi) for water), and n the initial porosity.
fmass
(float)Fluid mass density hPerm
,vPerm
(float)Permeability coefficient in horizontal and vertical directions respectively. b1
,b2
(float)Optional gravity acceleration components in horizontal and vertical directions respectively (defaults are 0.0) t
(float)Optional uniform element normal traction, positive in tension (default is 0.0)
See also
Brick up ElementÂ¶
BrickUP is an 8node hexahedral linear isoparametric element. Each node has 4 degreesoffreedom (DOF): DOFs 1 to 3 for solid displacement (u) and DOF 4 for fluid pressure (p). This element is implemented for simulating dynamic response of solidfluid fully coupled material, based on Biotâs theory of porous medium.

element
('brickUP', eleTag, *eleNodes, matTag, bulk, fmass, permX, permY, permZ, <bX=0, bY=0, bZ=0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of eight element nodes matTag
(int)Tag of an NDMaterial object (previously defined) of which the element is composed bulk
(float)Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: \(B_c \approx B_f/n\)
where \(B_f\) is the bulk modulus of fluid phase (\(2.2\times 10^6\) kPa (or \(3.191\times 10^5\) psi) for water), and n the initial porosity.
fmass
(float)Fluid mass density permX
,permY
,permZ
(float)Permeability coefficients in x, y, and z directions respectively. bX
,bY
,bZ
(float)Optional gravity acceleration components in x, y, and z directions directions respectively (defaults are 0.0)
See also
BbarQuad up ElementÂ¶
bbarQuadUP is a fournode planestrain mixed volume/pressure element, which uses a trilinear isoparametric formulation. This element is implemented for simulating dynamic response of solidfluid fully coupled material, based on Biotâs theory of porous medium. Each element node has 3 degreesoffreedom (DOF): DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p).

element
('bbarQuadUP', eleTag, *eleNodes, thick, matTag, bulk, fmass, hPerm, vPerm, <b1=0, b2=0, t=0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order thick
(float)Element thickness matTag
(int)Tag of an NDMaterial object (previously defined) of which the element is composed bulk
(float)Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: \(B_c \approx B_f/n\)
where \(B_f\) is the bulk modulus of fluid phase (\(2.2\times 10^6\) kPa (or \(3.191\times 10^5\) psi) for water), and n the initial porosity.
fmass
(float)Fluid mass density hPerm
,vPerm
(float)Permeability coefficient in horizontal and vertical directions respectively. b1
,b2
(float)Optional gravity acceleration components in horizontal and vertical directions respectively (defaults are 0.0) t
(float)Optional uniform element normal traction, positive in tension (default is 0.0)
See also
BbarBrick up ElementÂ¶
bbarBrickUP is a 8node mixed volume/pressure element, which uses a trilinear isoparametric formulation.
Each node has 4 degreesoffreedom (DOF): DOFs 1 to 3 for solid displacement (u) and DOF 4 for fluid pressure (p). This element is implemented for simulating dynamic response of solidfluid fully coupled material, based on Biotâs theory of porous medium.

element
('bbarBrickUP', eleTag, *eleNodes, matTag, bulk, fmass, permX, permY, permZ, <bX=0, bY=0, bZ=0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of eight element nodes matTag
(int)Tag of an NDMaterial object (previously defined) of which the element is composed bulk
(float)Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: \(B_c \approx B_f/n\)
where \(B_f\) is the bulk modulus of fluid phase (\(2.2\times 10^6\) kPa (or \(3.191\times 10^5\) psi) for water), and n the initial porosity.
fmass
(float)Fluid mass density permX
,permY
,permZ
(float)Permeability coefficients in x, y, and z directions respectively. bX
,bY
,bZ
(float)Optional gravity acceleration components in x, y, and z directions directions respectively (defaults are 0.0)
See also
Nine Four Node Quad up ElementÂ¶
Nine_Four_Node_QuadUP is a 9node quadrilateral planestrain element. The four corner nodes have 3 degreesoffreedom (DOF) each: DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p). The other five nodes have 2 DOFs each for solid displacement. This element is implemented for simulating dynamic response of solidfluid fully coupled material, based on Biotâs theory of porous medium.

element
('9_4_QuadUP', eleTag, *eleNodes, thick, matTag, bulk, fmass, hPerm, vPerm, <b1=0, b2=0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of nine element nodes thick
(float)Element thickness matTag
(int)Tag of an NDMaterial object (previously defined) of which the element is composed bulk
(float)Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: \(B_c \approx B_f/n\)
where \(B_f\) is the bulk modulus of fluid phase (\(2.2\times 10^6\) kPa (or \(3.191\times 10^5\) psi) for water), and n the initial porosity.
fmass
(float)Fluid mass density hPerm
,vPerm
(float)Permeability coefficient in horizontal and vertical directions respectively. b1
,b2
(float)Optional gravity acceleration components in horizontal and vertical directions respectively (defaults are 0.0)
See also
Twenty Eight Node Brick up ElementÂ¶
Twenty_Eight_Node_BrickUP is a 20node hexahedral isoparametric element.
The eight corner nodes have 4 degreesoffreedom (DOF) each: DOFs 1 to 3 for solid displacement (u) and DOF 4 for fluid pressure (p). The other nodes have 3 DOFs each for solid displacement. This element is implemented for simulating dynamic response of solidfluid fully coupled material, based on Biotâs theory of porous medium.

element
('20_8_BrickUP', eleTag, *eleNodes, matTag, bulk, fmass, permX, permY, permZ, <bX=0, bY=0, bZ=0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of twenty element nodes matTag
(int)Tag of an NDMaterial object (previously defined) of which the element is composed bulk
(float)Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: \(B_c \approx B_f/n\)
where \(B_f\) is the bulk modulus of fluid phase (\(2.2\times 10^6\) kPa (or \(3.191\times 10^5\) psi) for water), and n the initial porosity.
fmass
(float)Fluid mass density permX
,permY
,permZ
(float)Permeability coefficients in x, y, and z directions respectively. bX
,bY
,bZ
(float)Optional gravity acceleration components in x, y, and z directions directions respectively (defaults are 0.0)
See also
Other up elementsÂ¶
SSPquadUP ElementÂ¶
This command is used to construct a SSPquadUP element object.

element
('SSPquadUP', eleTag, *eleNodes, matTag, thick, fBulk, fDen, k1, k2, void, alpha, <b1=0.0, b2=0.0>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of four element nodes in counterclockwise order matTag
(int)unique integer tag associated with previouslydefined nDMaterial object thick
(float)thickness of the element in outofplane direction fBulk
(float)bulk modulus of the pore fluid fDen
(float)mass density of the pore fluid k1
k2
(float)permeability coefficients in global x and ydirections, respectively void
(float)voids ratio alpha
(float)spatial pressure field stabilization parameter (see discussion below for more information) b1
b2
(float)constant body forces in global x and ydirections, respectively (optional, default = 0.0)  See Note 3 The SSPquadUP element is an extension of the SSPquad Element for use in dynamic plane strain analysis of fluid saturated porous media. A mixed displacementpressure (up) formulation is used, based upon the work of Biot as extended by Zienkiewicz and Shiomi (1984).
The physical stabilization necessary to allow for reduced integration incorporates an assumed strain field in which the volumetric dilation and the shear strain associated with the the hourglass modes are zero, resulting in an element which is free from volumetric and shear locking. The elimination of shear locking results in greater coarse mesh accuracy in bending dominated problems, and the elimination of volumetric locking improves accuracy in nearlyincompressible problems. Analysis times are generally faster than corresponding full integration elements.
Equalorder interpolation is used for the displacement and pressure fields, thus, the SSPquadUP element does not inherently pass the infsup condition, and is not fully acceptable in the incompressibleimpermeable limit (the QuadUP Element has the same issue). A stabilizing parameter is employed to permit the use of equalorder interpolation for the SSPquadUP element. This parameter $alpha can be computed as
where h is the element size, c is the speed of elastic wave propagation in the solid phase, and den is the mass density of the solid phase. The $alpha parameter should be a small number. With a properly defined $alpha parameter, the SSPquadUP element can produce comparable results to a higherorder element such as the 9_4_QuadUP Element at a significantly lower computational cost and with a greater ease in mesh generation.
The full formulation for the SSPquadUP element can be found in McGann et al. (2012) along with several example applications.
Note
 The SSPquadUP element will only work in dynamic analysis.
 For saturated soils, the mass density input into the associated nDMaterial object should be the saturated mass density.
 When modeling soil, the body forces input into the SSPquadUP element should be the components of the gravitational vector, not the unit weight.
 Fixing the pore pressure degreeoffreedom (dof 3) at a node is a drainage boundary condition at which zero pore pressure will be maintained throughout the analysis. Leaving the third dof free allows pore pressures to build at that node.
 Valid queries to the SSPquadUP element when creating an ElementalRecorder object correspond to those for the nDMaterial object assigned to the element (e.g., âstressâ, âstrainâ). Material response is recorded at the single integration point located in the center of the element.
 The SSPquadUP element was designed with intentions of duplicating the functionality of the QuadUP Element. If an example is found where the SSPquadUP element cannot do something that works for the QuadUP Element, e.g., material updating, please contact the developers listed below so the bug can be fixed.
See also
SSPbrickUP ElementÂ¶
This command is used to construct a SSPbrickUP element object.

element
('SSPbrickUP', eleTag, *eleNodes, matTag, fBulk, fDen, k1, k2, k3, void, alpha, <b1, b2, b3>) eleTag
(int)unique element object tag eleNodes
(list (int))a list of eight element nodes in counterclockwise order matTag
(float)unique integer tag associated with previouslydefined nDMaterial object fBulk
(float)bulk modulus of the pore fluid fDen
(float)mass density of the pore fluid k1
k2
k3
(float)permeability coefficients in global x, y, and zdirections, respectively void
(float)voids ratio alpha
(float)spatial pressure field stabilization parameter (see discussion below for more information) b1
b2
b3
(float)constant body forces in global x, y, and zdirections, respectively (optional, default = 0.0)  See Note 3
The SSPbrickUP element is an extension of the SSPbrick Element for use in dynamic 3D analysis of fluid saturated porous media. A mixed displacementpressure (up) formulation is used, based upon the work of Biot as extended by Zienkiewicz and Shiomi (1984).
The physical stabilization necessary to allow for reduced integration incorporates an enhanced assumed strain field, resulting in an element which is free from volumetric and shear locking. The elimination of shear locking results in greater coarse mesh accuracy in bending dominated problems, and the elimination of volumetric locking improves accuracy in nearlyincompressible problems. Analysis times are generally faster than corresponding full integration elements.
Equalorder interpolation is used for the displacement and pressure fields, thus, the SSPbrickUP element does not inherently pass the infsup condition, and is not fully acceptable in the incompressibleimpermeable limit (the brickUP Element has the same issue). A stabilizing parameter is employed to permit the use of equalorder interpolation for the SSPbrickUP element. This parameter $alpha can be computed as
where \(h\) is the element size, and \(K_s\) and \(G_s\) are the bulk and shear moduli for the solid phase. The \(\alpha\) parameter should be a small number. With a properly defined \(\alpha\) parameter, the SSPbrickUP element can produce comparable results to a higherorder element such as the 20_8_BrickUP Element at a significantly lower computational cost and with a greater ease in mesh generation.
Note
 The SSPbrickUP element will only work in dynamic analysis.
 For saturated soils, the mass density input into the associated nDMaterial object should be the saturated mass density.
 When modeling soil, the body forces input into the SSPbrickUP element should be the components of the gravitational vector, not the unit weight.
 Fixing the pore pressure degreeoffreedom (dof 4) at a node is a drainage boundary condition at which zero pore pressure will be maintained throughout the analysis. Leaving the fourth dof free allows pore pressures to build at that node.
 Valid queries to the SSPbrickUP element when creating an ElementalRecorder object correspond to those for the nDMaterial object assigned to the element (e.g., âstressâ, âstrainâ). Material response is recorded at the single integration point located in the center of the element.
 The SSPbrickUP element was designed with intentions of duplicating the functionality of the brickUP Element. If an example is found where the SSPbrickUP element cannot do something that works for the brickUP Element, e.g., material updating, please contact the developers listed below so the bug can be fixed.
See also
Contact ElementsÂ¶
SimpleContact2DÂ¶
This command is used to construct a SimpleContact2D element object.

element
('SimpleContact2D', eleTag, iNode, jNode, cNode, lNode, matTag, gTol, fTol) eleTag
(int)unique element object tag iNode
jNode
(int)retained nodes (ndm 2 ndf 2) cNode
(int)constrained node (ndm 2 ndf 2) lNode
(int)Lagrange multiplier node (ndm 2 ndf 2) matTag
(int)unique integer tag associated with previouslydefined nDMaterial object gTol
(float)gap tolerance fTol
(float)force tolerance
The SimpleContact2D element is a twodimensional nodetosegment contact element which defines a frictional contact interface between two separate bodies. The master nodes are the nodes which define the endpoints of a line segment on the first body, and the slave node is a node from the second body. The Lagrange multiplier node is required to enforce the contact condition. This node should not be shared with any other element in the domain. Information on the theory behind this element can be found in, e.g. Wriggers (2002).
Note
 The SimpleContact2D element has been written to work exclusively with the ContactMaterial2D nDMaterial object.
 The valid recorder queries for this element are:
 force  returns the contact force acting on the slave node in vector form.
 frictionforce  returns the frictional force acting on the slave node in vector form.
 forcescalar  returns the scalar magnitudes of the normal and tangential contact forces.
 The SimpleContact2D elements are set to consider frictional behavior as a default, but the frictional state of the SimpleContact2D element can be changed from the input file using the setParameter command. When updating, value of 0 corresponds to the frictionless condition, and a value of 1 signifies the inclusion of friction. An example command for this update procedure is provided below
 The SimpleContact2D element works well in static and pseudostatic analysis situations.
 In transient analysis, the presence of the contact constraints can effect the stability of commonlyused time integration methods in the HHT or Newmark family (e.g., Laursen, 2002). For this reason, use of alternative timeintegration methods which numerically damp spurious high frequency behavior may be required. The TRBDF2 integrator is an effective method for this purpose. The Newmark integrator can also be effective with proper selection of the gamma and beta coefficients. The trapezoidal rule, i.e., Newmark with gamma = 0.5 and beta = 0.25, is particularly prone to instability related to the contact constraints and is not recommended.
See also
SimpleContact3DÂ¶
This command is used to construct a SimpleContact3D element object.

element
('SimpleContact3D', eleTag, iNode, jNode, kNode, lNode, cNode, lagr_node, matTag, gTol, fTol) eleTag
(int)unique element object tag iNode
jNode
kNode
lNode
(int)master nodes (ndm 3 ndf 3) cNode
(int)constrained node (ndm 3 ndf 3) lagr_node
(int)Lagrange multiplier node (ndm 3 ndf 3) matTag
(int)unique integer tag associated with previouslydefined nDMaterial object gTol
(float)gap tolerance fTol
(float)force tolerance
The SimpleContact3D element is a threedimensional nodetosurface contact element which defines a frictional contact interface between two separate bodies. The master nodes are the nodes which define a surface of a hexahedral element on the first body, and the slave node is a node from the second body. The Lagrange multiplier node is required to enforce the contact condition. This node should not be shared with any other element in the domain. Information on the theory behind this element can be found in, e.g. Wriggers (2002).
Note
 The SimpleContact3D element has been written to work exclusively with the ContactMaterial3D nDMaterial object.
 The valid recorder queries for this element are:
 force  returns the contact force acting on the slave node in vector form.
 frictionforce  returns the frictional force acting on the slave node in vector form.
 forcescalar  returns the scalar magnitudes of the single normal and two tangential contact forces.
 The SimpleContact3D elements are set to consider frictional behavior as a default, but the frictional state of the SimpleContact3D element can be changed from the input file using the setParameter command. When updating, value of 0 corresponds to the frictionless condition, and a value of 1 signifies the inclusion of friction. An example command for this update procedure is provided below
 The SimpleContact3D element works well in static and pseudostatic analysis situations.
 In transient analysis, the presence of the contact constraints can effect the stability of commonlyused time integration methods in the HHT or Newmark family (e.g., Laursen, 2002). For this reason, use of alternative timeintegration methods which numerically damp spurious high frequency behavior may be required. The TRBDF2 integrator is an effective method for this purpose. The Newmark integrator can also be effective with proper selection of the gamma and beta coefficients. The trapezoidal rule, i.e., Newmark with gamma = 0.5 and beta = 0.25, is particularly prone to instability related to the contact constraints and is not recommended.
See also
BeamContact2DÂ¶
This command is used to construct a BeamContact2D element object.

element
('BeamContact2D', eleTag, iNode, jNode, sNode, lNode, matTag, width, gTol, fTol, <cFlag>) eleTag
(int)unique element object tag iNode
jNode
(int)master nodes (ndm 2 ndf 3) sNode
(int)slave node (ndm 2 ndf 2) lNode
(int)Lagrange multiplier node (ndm 2 ndf 2) matTag
(int)unique integer tag associated with previouslydefined nDMaterial object width
(float)the width of the wall represented by the beam element in plane strain gTol
(float)gap tolerance fTol
(float)force tolerance cFlag
(int)optional initial contact flag
cFlag
= 0 >> contact between bodies is initially assumed (DEFAULT)cFlag
= 1 >> no contact between bodies is initially assumed
The BeamContact2D element is a twodimensional beamtonode contact element which defines a frictional contact interface between a beam element and a separate body. The master nodes (3 DOF) are the endpoints of the beam element, and the slave node (2 DOF) is a node from a second body. The Lagrange multiplier node (2 DOF) is required to enforce the contact condition. Each contact element should have a unique Lagrange multiplier node. The Lagrange multiplier node should not be fixed, otherwise the contact condition will not work.
Under plane strain conditions in 2D, a beam element represents a unit thickness of a wall. The width is the dimension of this wall in the 2D plane. This width should be builtin to the model to ensure proper enforcement of the contact condition. The Excavation Supported by Cantilevered Sheet Pile Wall practical example provides some further examples and discussion on the usage of this element.
Note
 The BeamContact2D element has been written to work exclusively with the ContactMaterial2D nDMaterial object.
 The valid recorder queries for this element are:
 force  returns the contact force acting on the slave node in vector form.
 frictionforce  returns the frictional force acting on the slave node in vector form.
 forcescalar  returns the scalar magnitudes of the normal and tangential contact forces.
 masterforce  returns the reactions (forces and moments) acting on the master nodes.
 The BeamContact2D elements are set to consider frictional behavior as a default, but the frictional state of the BeamContact2D element can be changed from the input file using the setParameter command. When updating, value of 0 corresponds to the frictionless condition, and a value of 1 signifies the inclusion of friction. An example command for this update procedure is provided below
 The BeamContact2D element works well in static and pseudostatic analysis situations.
 In transient analysis, the presence of the contact constraints can effect the stability of commonlyused time integration methods in the HHT or Newmark family (e.g., Laursen, 2002). For this reason, use of alternative timeintegration methods which numerically damp spurious high frequency behavior may be required. The TRBDF2 integrator is an effective method for this purpose. The Newmark integrator can also be effective with proper selection of the gamma and beta coefficients. The trapezoidal rule, i.e., Newmark with gamma = 0.5 and beta = 0.25, is particularly prone to instability related to the contact constraints and is not recommended.
See also
BeamContact3DÂ¶
This command is used to construct a BeamContact3D element object.

element
('BeamContact3D', eleTag, iNode, jNode, cNode, lNode, radius, crdTransf, matTag, gTol, fTol, <cFlag>) eleTag
(int)unique element object tag iNode
jNode
(int)master nodes (ndm 3 ndf 6) cNode
(int)constrained node (ndm 3 ndf 3) lNode
(int)Lagrange multiplier node (ndm 3 ndf 3) radius
(float)constant radius of circular beam associated with beam element crdTransf
(int)unique integer tag associated with previouslydefined geometricTransf object matTag
(int)unique integer tag associated with previouslydefined nDMaterial object gTol
(float)gap tolerance fTol
(float)force tolerance cFlag
(int)optional initial contact flag
cFlag
= 0 >> contact between bodies is initially assumed (DEFAULT)cFlag
= 1 >> no contact between bodies is initially assumed
The BeamContact3D element is a threedimensional beamtonode contact element which defines a frictional contact interface between a beam element and a separate body. The master nodes (6 DOF) are the endpoints of the beam element, and the slave node (3 DOF) is a node from a second body. The Lagrange multiplier node (3 DOF) is required to enforce the contact condition. Each contact element should have a unique Lagrange multiplier node. The Lagrange multiplier node should not be fixed, otherwise the contact condition will not work.
Note
 The BeamContact3D element has been written to work exclusively with the ContactMaterial3D nDMaterial object.
 The valid recorder queries for this element are:
 force  returns the contact force acting on the slave node in vector form.
 frictionforce  returns the frictional force acting on the slave node in vector form.
 forcescalar  returns the scalar magnitudes of the single normal and two tangential contact forces.
 masterforce  returns the reactions (forces only) acting on the master nodes.
 mastermoment  returns the reactions (moments only) acting on the master nodes.
 masterreaction  returns the full reactions (forces and moments) acting on the master nodes.
 The BeamContact3D elements are set to consider frictional behavior as a default, but the frictional state of the BeamContact3D element can be changed from the input file using the setParameter command. When updating, value of 0 corresponds to the frictionless condition, and a value of 1 signifies the inclusion of friction. An example command for this update procedure is provided below
 The BeamContact3D element works well in static and pseudostatic analysis situations.
 In transient analysis, the presence of the contact constraints can effect the stability of commonlyused time integration methods in the HHT or Newmark family (e.g., Laursen, 2002). For this reason, use of alternative timeintegration methods which numerically damp spurious high frequency behavior may be required. The TRBDF2 integrator is an effective method for this purpose. The Newmark integrator can also be effective with proper selection of the gamma and beta coefficients. The trapezoidal rule, i.e., Newmark with gamma = 0.5 and beta = 0.25, is particularly prone to instability related to the contact constraints and is not recommended.
See also
BeamEndContact3DÂ¶
This command is used to construct a BeamEndContact3D element object.

element
('BeamEndContact3D', eleTag, iNode, jNode, cNode, lNode, radius, gTol, fTol, <cFlag>) eleTag
(int)unique element object tag iNode
(int)master node from the beam (ndm 3 ndf 6) jNode
(int)the remaining node on the beam element with iNode
(ndm 3 ndf 6)cNode
(int)constrained node (ndm 3 ndf 3) lNode
(int)Lagrange multiplier node (ndm 3 ndf 3) radius
(float)radius of circular beam associated with beam element gTol
(float)gap tolerance fTol
(float)force tolerance cFlag
(float)optional initial contact flag
cFlag
= 0 >> contact between bodies is initially assumed (DEFAULT)cFlag1
= 1 >> no contact between bodies is initially assumed
The BeamEndContact3D element is a nodetosurface contact element which defines a normal contact interface between the end of a beam element and a separate body. The first master node ($iNode) is the beam node which is at the end of the beam (i.e. only connected to a single beam element), the second node ($jNode) is the remaining node on the beam element in question. The slave node is a node from a second body. The Lagrange multiplier node is required to enforce the contact condition. This node should not be shared with any other element in the domain, and should be created with the same number of DOF as the slave node.
The BeamEndContact3D element enforces a contact condition between a fictitious circular plane associated with a beam element and a node from a second body. The normal direction of the contact plane coincides with the endpoint tangent of the beam element at the master beam node ($iNode). The extents of this circular plane are defined by the radius input parameter. The master beam node can only come into contact with a slave node which is within the extents of the contact plane. There is a lag step associated with changing between the âin contactâ and ânot in contactâ conditions.
This element was developed for use in establishing a contact condition for the tip of a pile modeled as using beam elements and the underlying soil elements in threedimensional analysis.
Note
 The BeamEndContact3D element does not use a material object.
 The valid recorder queries for this element are:
 force  returns the contact force acting on the slave node in vector form.
 masterforce  returns the reactions (forces and moments) acting on the master node.
 The BeamEndContact3D element works well in static and pseudostatic analysis situations.
 In transient analysis, the presence of the contact constraints can effect the stability of commonlyused time integration methods in the HHT or Newmark family (e.g., Laursen, 2002). For this reason, use of alternative timeintegration methods which numerically damp spurious high frequency behavior may be required. The TRBDF2 integrator is an effective method for this purpose. The Newmark integrator can also be effective with proper selection of the gamma and beta coefficients. The trapezoidal rule, i.e., Newmark with gamma = 0.5 and beta = 0.25, is particularly prone to instability related to the contact constraints and is not recommended.
See also
Cable ElementsÂ¶
CatenaryCableElementÂ¶
This command is used to construct a catenary cable element object.

element
('CatenaryCable', eleTag, iNode, jNode, weight, E, A, L0, alpha, temperature_change, rho, errorTol, Nsubsteps, massType) eleTag
(int)unique element object tag iNode
jNode
(int)end nodes (3 dof per node) weight
(float)undefined E
(float)elastic modulus of the cable material A
(float)crosssectional area of element L0
(float)unstretched length of the cable alpha
(float)coefficient of thermal expansion temperature_change
(float)temperature change for the element rho
(float)mass per unit length errorTol
(float)allowed tolerance for withinelement equilbrium (NewtonRhapson iterations) Nsubsteps
(int)number of withinelement substeps into which equilibrium iterations are subdivided (not number of steps to convergence) massType
(int)Mass matrix model to use ( massType
= 0 lumped mass matrix,massType
= 1 rigidbody mass matrix (in development))
This cable is a flexibilitybased formulation of the catenary cable. An iterative scheme is used internally to compute equilibrium. At each iteration, node i is considered fixed while node j is free. Endforces are applied at nodej and its displacements computed. Corrections to these forces are applied iteratively using a NewtonRhapson scheme (with optional substepping via $Nsubsteps) until nodal displacements are within the provided tolerance ($errortol). When convergence is reached, a stiffness matrix is computed by inversion of the flexibility matrix and rigidbody mode injection.
Note
 The stiffness of the cable comes from the largedeformation interaction between loading and cable shape. Therefore, all cables must have distributed forces applied to them. See example. Should not work for only nodal forces.
 Valid queries to the CatenaryCable element when creating an ElementalRecorder object correspond to âforcesâ, which output the endforces of the element in global coordinates (3 for each node).
 Only the lumpedmass formulation is currently available.
 The element does up 100 internal iterations. If convergence is not achieved, will result in error and some diagnostic information is printed out.
See also
PFEM ElementsÂ¶
PFEMElementBubbleÂ¶

element
('PFEMElementBubble', eleTag, *eleNodes, rho, mu, b1, b2, <b3>, <thickness, kappa>) Create a PFEM Bubble element, which is a fluid element for FSI analysis.
eleTag
(int)tag of the element eleNodes
(list (int))A list of three or four element nodes, four are required for 3D nd4
(int)tag of node 4 (required for 3D) rho
(float)fluid density mu
(float)fluid viscosity b1
(float)body body acceleration in x direction b2
(float)body body acceleration in y direction b3
(float)body body acceleration in z direction (required for 3D) thickness
(float)element thickness (required for 2D) kappa
(float)fluid bulk modulus (optional)
PFEMElementCompressibleÂ¶

element
('PFEMElementCompressible', eleTag, *eleNodes, rho, mu, b1, b2, <thickness, kappa>) Create a PFEM compressible element, which is a fluid element for FSI analysis.
eleTag
(int)tag of the element eleNodes
(list (int))A list of four element nodes, last one is middle node rho
(float)fluid density mu
(float)fluid viscosity b1
(float)body body acceleration in x direction b2
(float)body body acceleration in y direction thickness
(float)element thickness (optional) kappa
(float)fluid bulk modulus (optional)
Misc.Â¶
SurfaceLoad ElementÂ¶
This command is used to construct a SurfaceLoad element object.

element
('SurfaceLoad', eleTag, *eleNodes, p) eleTag
(int)unique element object tag eleNodes
(list (int))the four nodes defining the element, input in counterclockwise order (ndm 3 ndf 3) p
(float)applied pressure loading normal to the surface, outward is positive, inward is negative
The SurfaceLoad element is a fournode element which can be used to apply surface pressure loading to 3D brick elements. The SurfaceLoad element applies energeticallyconjugate forces corresponding to the input scalar pressure to the nodes associated with the element. As these nodes are shared with a 3D brick element, the appropriate nodal loads are therefore applied to the brick.
Note
 There are no valid ElementalRecorder queries for the SurfaceLoad element. Its sole purpose is to apply nodal forces to the adjacent brick element.
 The pressure loading from the SurfaceLoad element can be applied in a load pattern. See the analysis example below.
See also
VS3D4Â¶
This command is used to construct a fournode 3D viscousspring boundary quad element object based on a bilinear isoparametric formulation.

element
('VS3D4', eleTag, *eleNodes, E, G, rho, R, alphaN, alphaT) eleTag
(int)unique element object tag eleNodes
(list (int))4 end nodes E
(float)Youngâs Modulus of element material G
(float)Shear Modulus of element material rho
(float)Mass Density of element material R
(float)distance from the scattered wave source to the boundary alphaN
(float)correction parameter in the normal direction alphaT
(float)correction parameter in the tangential direction
Note
Reference: Liu J, Du Y, Du X, et al. 3D viscousspring artificial boundary in time domain. Earthquake Engineering and Engineering Vibration, 2006, 5(1):93102
See also
AC3D8Â¶
This command is used to construct an eightnode 3D brick acoustic element object based on a trilinear isoparametric formulation.

element
('AC3D8', eleTag, *eleNodes, matTag) eleTag
(int)unique element object tag eleNodes
(list (int))8 end nodes matTag
(int)Material Tag of previously defined nD material
Note
Reference: ABAQUS theory manual. (2.9.1 Coupled acousticstructural medium analysis)
See also
ASI3D8Â¶
This command is used to construct an eightnode zerothickness 3D brick acousticstructure interface element object based on a bilinear isoparametric formulation. The nodes in the acoustic domain share the same coordinates with the nodes in the solid domain.

element
('ASI3D8', eleTag, *eleNodes1, *eleNodes2) eleTag
(int)unique element object tag *eleNodes1
(list (int))four nodes defining structure domain of element boundaries *eleNodes2
(list (int))four nodes defining acoustic domain of element boundaries
Note
Reference: ABAQUS theory manual. (2.9.1 Coupled acousticstructural medium analysis)
See also
AV3D4Â¶
This command is used to construct a fournode 3D acoustic viscous boundary quad element object based on a bilinear isoparametric formulation.

element
('AV3D4', eleTag, *eleNodes, matTag) eleTag
(int)unique element object tag eleNodes
(list (int))4 end nodes matTag
(int)Material Tag of previously defined nD material
See also
node commandÂ¶

node
(nodeTag, *crds, 'ndf', ndf, 'mass', *mass, 'disp', *disp, 'vel', *vel, 'accel', *accel)Â¶ Create a OpenSees node.
nodeTag
(int)node tag. crds
(list (float))nodal coordinates. ndf
(float)nodal ndf. (optional) mass
(list (float))nodal mass. (optional) vel
(list (float))nodal velocities. (optional) accel
(list (float))nodal accelerations. (optional)
sp constraint commandsÂ¶
Create constraints for a single dof of a node.
fix commandÂ¶

fix
(nodeTag, *constrValues)Â¶ Create a homogeneous SP constriant.
nodeTag
(int)tag of node to be constrained constrValues
(list (int))a list of constraint values (0 or 1), must be preceded with
*
.0
free1
fixed
For example,
# fully fixed
vals = [1,1,1]
fix(nodeTag, *vals)
fixX commandÂ¶
fixY commandÂ¶
mp constraint commandsÂ¶
Create constraints for multiple dofs of multiple nodes.
equalDOF commandÂ¶

equalDOF
(rNodeTag, cNodeTag, *dofs)Â¶ Create a multipoint constraint between nodes.
rNodeTag
(int)integer tag identifying the retained, or master node. cNodeTag
(int)integer tag identifying the constrained, or slave node. dofs
(list (int))nodal degreesoffreedom that are constrained at the cNode to be the same as those at the rNode Valid range is from 1 through ndf, the number of nodal degreesoffreedom.
equalDOF_Mixed commandÂ¶

equalDOF_Mixed
(rNodeTag, cNodeTag, numDOF, *rcdofs)Â¶ Create a multipoint constraint between nodes.
rNodeTag
(int)integer tag identifying the retained, or master node. cNodeTag
(int)integer tag identifying the constrained, or slave node. numDOF
(int)number of dofs to be constrained rcdofs
(list (int))nodal degreesoffreedom that are constrained at the cNode to be the same as those at the rNode Valid range is from 1 through ndf, the number of nodal degreesoffreedom.
rcdofs = [rdof1, cdof1, rdof2, cdof2, ...]
rigidDiaphragm commandÂ¶

rigidDiaphragm
(perpDirn, rNodeTag, *cNodeTags)Â¶ Create a multipoint constraint between nodes. These objects will constraint certain degreesoffreedom at the listed slave nodes to move as if in a rigid plane with the master node. To enforce this constraint,
Transformation
constraint is recommended.perpDirn
(int)direction perpendicular to the rigid plane (i.e. direction 3 corresponds to the 12 plane) rNodeTag
(int)integer tag identifying the master node cNodeTags
(list (int))integar tags identifying the slave nodes
rigidLink commandÂ¶

rigidLink
(type, rNodeTag, cNodeTag)Â¶ Create a multipoint constraint between nodes.
type
(str)stringbased argument for rigidlink type:
'bar'
: only the translational degreeoffreedom will be constrained to be exactly the same as those at the master node'beam'
: both the translational and rotational degrees of freedom are constrained.
rNodeTag
(int)integer tag identifying the master node cNodeTag
(int)integar tag identifying the slave node
timeSeries commandsÂ¶

timeSeries
(tsType, tsTag, *tsArgs)Â¶ This command is used to construct a TimeSeries object which represents the relationship between the time in the domain, \(t\), and the load factor applied to the loads, \(\lambda\), in the load pattern with which the TimeSeries object is associated, i.e. \(\lambda = F(t)\).
tsType
(str)time series type. tsTag
(int)time series tag. tsArgs
(list)a list of time series arguments
The following contain information about available tsType
:
 Constant TimeSeries
 Linear TimeSeries
 Trigonometric TimeSeries
 Triangular TimeSeries
 Rectangular TimeSeries
 Pulse TimeSeries
 Path TimeSeries
Constant TimeSeriesÂ¶

timeSeries
('Constant', tag, 'factor', factor=1.0) This command is used to construct a TimeSeries object in which the load factor applied remains constant and is independent of the time in the domain, i.e. \(\lambda = f(t) = C\).
tag
(int)unique tag among TimeSeries objects. factor
(float)the load factor applied (optional)
Linear TimeSeriesÂ¶

timeSeries
('Linear', tag, 'factor', factor=1.0) This command is used to construct a TimeSeries object in which the load factor applied is linearly proportional to the time in the domain, i.e.
\(\lambda = f(t) = cFactor * t\).
tag
(int)unique tag among TimeSeries objects. factor
(float)Linear factor. (optional)
Trigonometric TimeSeriesÂ¶

timeSeries
('Trig', tag, tStart, tEnd, period, 'factor', factor=1.0, 'shift', shift=0.0, 'zeroShift', zeroShift=0.0) This command is used to construct a TimeSeries object in which the load factor is some trigonemtric function of the time in the domain
\[ \begin{align}\begin{aligned}\begin{split}\lambda = f(t) = \begin{cases} cFactor * sin(\frac{2.0\pi(ttStart)}{period}+\phi), & tStart<=t<=tEnd\\ 0.0, & otherwise \end{cases}\end{split}\\\phi = shift  \frac{period}{2.0\pi} * \arcsin(\frac{zeroShift}{cFactor})\end{aligned}\end{align} \]tag
(int)unique tag among TimeSeries objects. tStart
(float)Starting time of nonzero load factor. tEnd
(float)Ending time of nonzero load factor. period
(float)Characteristic period of sine wave. shift
(float)Phase shift in radians. (optional) factor
(float)Load factor. (optional) zeroShift
(float)Zero shift. (optional)
Triangular TimeSeriesÂ¶

timeSeries
('Triangle', tag, tStart, tEnd, period, 'factor', factor=1.0, 'shift', shift=0.0, 'zeroShift', zeroShift=0.0) This command is used to construct a TimeSeries object in which the load factor is some triangular function of the time in the domain.
\[\begin{split}\lambda = f(t) = \begin{cases} slope*k*period+zeroShift, & k < 0.25\\ cFactorslope*(k0.25)*period+zeroShift, & k < 0.75\\ cFactor+slope*(k0.75)*period+zeroShift, & k < 1.0\\ 0.0, & otherwise \end{cases}\end{split}\]\[ \begin{align}\begin{aligned}slope = \frac{cFactor}{period/4}\\k = \frac{t+\phitStart}{period}floor(\frac{t+\phitStart}{period})\\\phi = shift  \frac{zeroShift}{slope}\end{aligned}\end{align} \]tag
(int)unique tag among TimeSeries objects. tStart
(float)Starting time of nonzero load factor. tEnd
(float)Ending time of nonzero load factor. period
(float)Characteristic period of sine wave. shift
(float)Phase shift in radians. (optional) factor
(float)Load factor. (optional) zeroShift
(float)Zero shift. (optional)
Rectangular TimeSeriesÂ¶

timeSeries
('Rectangular', tag, tStart, tEnd, 'factor', factor=1.0) This command is used to construct a TimeSeries object in which the load factor is constant for a specified period and 0 otherwise, i.e.
\[\begin{split}\lambda = f(t) = \begin{cases} cFactor, & tStart<=t<=tEnd\\ 0.0, & otherwise \end{cases}\end{split}\]tag
(int)unique tag among TimeSeries objects. tStart
(float)Starting time of nonzero load factor. tEnd
(float)Ending time of nonzero load factor. factor
(float)Load factor. (optional)
Pulse TimeSeriesÂ¶

timeSeries
('Pulse', tag, tStart, tEnd, period, 'width', width=0.5, 'shift', shift=0.0, 'factor', factor=1.0, 'zeroShift', zeroShift=0.0) This command is used to construct a TimeSeries object in which the load factor is some pulse function of the time in the domain.
\[\begin{split}\lambda = f(t) = \begin{cases} cFactor+zeroShift, & k < width\\ zeroshift, & k < 1\\ 0.0, & otherwise \end{cases}\end{split}\]\[k = \frac{t+shifttStart}{period}floor(\frac{t+shifttStart}{period})\]tag
(int)unique tag among TimeSeries objects. tStart
(float)Starting time of nonzero load factor. tEnd
(float)Ending time of nonzero load factor. period
(float)Characteristic period of pulse. width
(float)Pulse width as a fraction of the period. (optinal) shift
(float)Phase shift in seconds. (optional) factor
(float)Load factor. (optional) zeroShift
(float)Zero shift. (optional)
Path TimeSeriesÂ¶

timeSeries
('Path', tag, 'dt', dt=0.0, 'values', *values, 'time', *time, 'filepath', filepath='', 'fileTime', fileTime='', 'factor', factor=1.0, 'startTime', startTime=0.0, 'useLast', 'prependZero') The relationship between load factor and time is input by the user as a series of discrete points in the 2d space (load factor, time). The input points can come from a file or from a list in the script. When the time specified does not match any of the input points, linear interpolation is used between points. There are many ways to specify the load path, for example, the load factors set with
values
orfilepath
, and the time set withdt
,time
, orfileTime
.tag
(int)unique tag among TimeSeries objects. dt
(float)Time interval between specified points. (optional) values
(list (float))Load factor values in a (list). (optional) time
(list (float))Time values in a (list). (optional) filepath
(str)File containing the load factors values. (optional) fileTime
(str)File containing the time values for corresponding load factors. (optional) factor
(float)A factor to multiply load factors by. (optional) startTime
(float)Provide a start time for provided load factors. (optional) 'useLast'
(str)Use last value after the end of the series. (optional) 'prependZero'
(str)Prepend a zero value to the series of load factors. (optional)  Linear interpolation between points.
 If the specified time is beyond last point (AND WATCH FOR NUMERICAL ROUNDOFF), 0.0 is returned. Specify
'useLast'
to use the last data point instead of 0.0.  The transient integration methods in OpenSees assume zero initial conditions. So it is important that any timeSeries that is being used in a transient analysis` starts from zero (first data point in the timeSeries = 0.0). To guarantee that this is the case the optional parameter
'prependZero'
can be specified to prepend a zero value to the provided TimeSeries.
pattern commandsÂ¶

pattern
(patternType, patternTag, *patternArgs)Â¶
The pattern command is used to construct a LoadPattern and add it to the Domain. Each LoadPattern in OpenSees has a TimeSeries associated with it. In addition it may contain ElementLoads, NodalLoads and SinglePointConstraints. Some of these SinglePoint constraints may be associated with GroundMotions.
patternType (str) 
pattern type. 
patternTag (int) 
pattern tag. 
patternArgs (list) 
a list of pattern arguments 
The following contain information about available patternType
:
Plain PatternÂ¶

pattern
('Plain', patternTag, tsTag, 'fact', fact) This commnand allows the user to construct a LoadPattern object. Each plain load pattern is associated with a TimeSeries object and can contain multiple NodalLoads, ElementalLoads and SP_Constraint objects. The command to generate LoadPattern object contains in { } the commands to generate all the loads and the singlepoint constraints in the pattern. To construct a load pattern and populate it, the following command is used:
patternTag
(int)unique tag among load patterns. tsTag
(int)the tag of the time series to be used in the load pattern fact
(float)constant factor. (optional)
Note
the commands below to generate all the loads and sp constraints will be included in last called pattern command.
load commandÂ¶

load
(nodeTag, *loadValues)Â¶ This command is used to construct a NodalLoad object and add it to the enclosing LoadPattern.
nodeTag
(int)tag of node to which load is applied. loadValues
(list (float))ndf reference load values.
Note
The load values are reference loads values. It is the time series that provides the load factor. The load factor times the reference values is the load that is actually applied to the node.
eleLoad commandÂ¶

eleLoad
('ele', *eleTags, 'range', eleTag1, eleTag2, 'type', 'beamUniform', Wy, Wz=0.0, Wx=0.0, 'beamPoint', Py, Pz=0.0, xL, Px=0.0, 'beamThermal', *tempPts)Â¶ The eleLoad command is used to construct an ElementalLoad object and add it to the enclosing LoadPattern.
eleTags
(list (int))tag of PREVIOUSLY DEFINED element eleTag1
(int)element tag eleTag2
(int)element tag Wx
(float)mag of uniformily distributed ref load acting in direction along member length. (optional) Wy
(float)mag of uniformily distributed ref load acting in local y direction of element Wz
(float)mag of uniformily distributed ref load acting in local z direction of element. (optional and only for 3D) Px
(float)mag of ref point load acting in direction along member length. (optional) Py
(float)mag of ref point load acting in local y direction of element Pz
(float)mag of ref point load acting in local z direction of element. (optional and only for 3D) xL
(float)location of point load relative to node I, prescribed as fraction of element length tempPts
(list (float))temperature points: temPts = [T1, y1, T2, y2, ..., T9, y9]
Each point(T1, y1)
define a temperature and location. This command may accept 2,5 or 9 temperature points.
Note
 The load values are reference loads values, it is the time sereries that provides the load factor. The load factor times the reference values is the load that is actually applied to the node.
 At the moment, eleLoads do not work with 3D beamcolumn elements if Corotational geometric transformation is used.
sp commandÂ¶

sp
(nodeTag, dof, *dofValues)Â¶ This command is used to construct a singlepoint constraint object and add it to the enclosing LoadPattern.
nodeTag
(int)tag of node to which load is applied. dof
(int)the degreeoffreedom at the node to which constraint is applied (1 through ndf) dofValues
(list (float))ndf reference constraint values.
Note
The dofValue is a reference value, it is the time series that provides the load factor. The load factor times the reference value is the constraint that is actually applied to the node.
UniformExcitation PatternÂ¶

pattern
('UniformExcitation', patternTag, dir, 'disp', dispSeriesTag, 'vel', velSeriesTag, 'accel', accelSeriesTag, 'vel0', vel0, 'fact', fact) The UniformExcitation pattern allows the user to apply a uniform excitation to a model acting in a certain direction. The command is as follows:
patternTag
(int)unique tag among load patterns dir
(int)direction in which ground motion acts
 corresponds to translation along the global X axis
 corresponds to translation along the global Y axis
 corresponds to translation along the global Z axis
 corresponds to rotation about the global X axis
 corresponds to rotation about the global Y axis
 corresponds to rotation about the global Z axis
dispSeriesTag
(int)tag of the TimeSeries series defining the displacement history. (optional) velSeriesTag
(int)tag of the TimeSeries series defining the velocity history. (optional) accelSeriesTag
(int)tag of the TimeSeries series defining the acceleration history. (optional) vel0
(float)the initial velocity (optional, default=0.0) fact
(float)constant factor (optional, default=1.0)
Note
 The responses obtained from the nodes for this type of excitation are RELATIVE values, and not the absolute values obtained from a multisupport case.
 must set one of the disp, vel or accel time series
MultiSupport Excitation PatternÂ¶

pattern
('MultipleSupport', patternTag) The MultiSupport pattern allows similar or different prescribed ground motions to be input at various supports in the structure. In OpenSees, the prescribed motion is applied using singlepoint constraints, the singlepoint constraints taking their constraint value from user created ground motions. =================================== ===========================================================================
patternTag
(int) integer tag identifying pattern =================================== ===========================================================================
Note
 The results for the responses at the nodes are the ABSOLUTE values, and not relative values as in the case of a UniformExciatation.
 The nonhomogeneous single point constraints require an appropriate choice of constraint handler.
Plain Ground MotionÂ¶

groundMotion
(gmTag, 'Plain', 'disp', dispSeriesTag, 'vel', velSeriesTag, 'accel', accelSeriesTag, 'int', tsInt='Trapezoidal', 'fact', factor=1.0)Â¶ This command is used to construct a plain GroundMotion object. Each GroundMotion object is associated with a number of TimeSeries objects, which define the acceleration, velocity and displacement records for that ground motion. T
gmTag
(int)unique tag among ground motions in load pattern dispSeriesTag
(int)tag of the TimeSeries series defining the displacement history. (optional) velSeriesTag
(int)tag of the TimeSeries series defining the velocity history. (optional) accelSeriesTag
(int)tag of the TimeSeries series defining the acceleration history. (optional) tsInt
(str)'Trapezoidal'
or'Simpson'
numerical integration methodfactor
(float)constant factor. (optional)
Note
 The displacements are the ones used in the ImposedMotions to set nodal response.
 If only the acceleration TimeSeries is provided, numerical integration will be used to determine the velocities and displacements.
 For earthquake excitations it is important that the user provide the displacement time history, as the one generated using the trapezoidal method will not provide good results.
 Any combination of the acceleration, velocity and displacement timeseries can be specified.
Interpolated Ground MotionÂ¶

groundMotion
(gmTag, 'Interpolated', *gmTags, 'fact', facts) This command is used to construct an interpolated GroundMotion object, where the motion is determined by combining several previously defined ground motions in the load pattern.
gmTag
(int)unique tag among ground motions in load pattern gmTags
(list (int))the tags of existing ground motions in pattern to be used for interpolation facts
(list (float))the interpolation factors. (optional)
Imposed MotionÂ¶

imposedMotion
(nodeTag, dof, gmTag)Â¶ This command is used to construct an ImposedMotionSP constraint which is used to enforce the response of a dof at a node in the model. The response enforced at the node at any give time is obtained from the GroundMotion object associated with the constraint.
nodeTag
(int)tag of node on which constraint is to be placed dof
(int)dof of enforced response. Valid range is from 1 through ndf at node. gmTag
(int)predefined GroundMotion object tag
mass commandÂ¶
region commandÂ¶

region
(regTag, 'ele', *eles, 'eleOnly', *eles, 'eleRange', startEle, endEle, 'eleOnlyRange', startEle, endEle, 'node', *nodes, 'nodeOnly', *nodes, 'nodeRange', startNode, endNode, 'nodeOnlyRange', startNode, endNode, 'rayleigh', alphaM, betaK, betaKinit, betaKcomm)Â¶ The region command is used to label a group of nodes and elements. This command is also used to assign rayleigh damping parameters to the nodes and elements in this region. The region is specified by either elements or nodes, not both. If elements are defined, the region includes these elements and the all connected nodes, unless the eleOnly option is used in which case only elements are included. If nodes are specified, the region includes these nodes and all elements of which all nodes are prescribed to be in the region, unless the nodeOnly option is used in which case only the nodes are included.
regTag
(int)unique integer tag eles
(list (int))tags of selected elements in domain to be included in region (optional) nodes
(list (int))tags of selected nodes in domain to be included in region (optional) startEle
(int)tag for start element (optional) endEle
(int)tag for end element (optional) startNode
(int)tag for start node (optional) endNode
(int)tag for end node (optional) alphaM
(float)factor applied to elements or nodes mass matrix (optional) betaK
(float)factor applied to elements current stiffness matrix (optional) betaKinit
(float)factor applied to elements initial stiffness matrix (optional) betaKcomm
(float)factor applied to elements committed stiffness matrix (optional)
Note
The user cannot prescribe the region by BOTH elements and nodes.
rayleigh commandÂ¶

rayleigh
(alphaM, betaK, betaKinit, betaKcomm)Â¶ This command is used to assign damping to all previouslydefined elements and nodes. When using rayleigh damping in OpenSees, the damping matrix for an element or node, D is specified as a combination of stiffness and massproportional damping matrices:
\[D = \alpha_M * M + \beta_K * K_{curr} + \beta_{Kinit} * K_{init} + \beta_{Kcomm} * K_{commit}\]alphaM
(float)factor applied to elements or nodes mass matrix betaK
(float)factor applied to elements current stiffness matrix. betaKinit
(float)factor applied to elements initial stiffness matrix. betaKcomm
(float)factor applied to elements committed stiffness matrix.
block commandsÂ¶
Create a block of mesh
block2D commandÂ¶

block2D
(numX, numY, startNode, startEle, eleType, *eleArgs, *crds)Â¶ Create mesh of quadrilateral elements
numX
(int)number of elements in local x directions of the block. numY
(int)number of elements in local y directions of the block. startNode
(int)node from which the mesh generation will start. startEle
(int)element from which the mesh generation will start. eleType
(str)element type ( 'quad'
,'shell'
,'bbarQuad'
,'enhancedQuad'
, or'SSPquad'
)eleArgs
(list)a list of element parameters. crds
(list)coordinates of the block elements with the format:
[1, x1, y1, <z1>,
2, x2, y2, <z2>,
3, x3, y3, <z3>,
4, x4, y4, <z4>,
<5>, <x5>, <y5>, <z5>,
<6>, <x6>, <y6>, <z6>,
<7>, <x7>, <y7>, <z7>,
<8>, <x8>, <y8>, <z8>,
<9>, <x9>, <y9>, <z9>]
<> means optional
block3D commandÂ¶

block3D
(numX, numY, numZ, startNode, startEle, eleType, *eleArgs, *crds)Â¶ Create mesh of quadrilateral elements
numX
(int)number of elements in local x directions of the block. numY
(int)number of elements in local y directions of the block. numZ
(int)number of elements in local z directions of the block. startNode
(int)node from which the mesh generation will start. startEle
(int)element from which the mesh generation will start. eleType
(str)element type ( 'stdBrick'
,'bbarBrick'
,'Brick20N'
)eleArgs
(list)a list of element parameters. crds
(list)coordinates of the block elements with the format:
[1, x1, y1, z1,
2, x2, y2, z2,
3, x3, y3, z3,
4, x4, y4, z4,
5, x5, y5, z5,
6, x6, y6, z6,
7, x7, y7, z7,
8, x8, y8, z8,
9, x9, y9, z9,
<10>, <x10>, <y10>, <z10>,
<11>, <x11>, <y11>, <z11>,
<12>, <x12>, <y12>, <z12>,
<13>, <x13>, <y13>, <z13>,
<14>, <x14>, <y14>, <z14>,
<15>, <x15>, <y15>, <z15>,
<16>, <x16>, <y16>, <z16>,
<17>, <x17>, <y17>, <z17>,
<18>, <x18>, <y18>, <z18>,
<19>, <x19>, <y19>, <z19>,
<20>, <x20>, <y20>, <z20>,
<21>, <x21>, <y21>, <z21>,
<22>, <x22>, <y22>, <z22>,
<23>, <x23>, <y23>, <z23>,
<24>, <x24>, <y24>, <z24>,
<25>, <x25>, <y25>, <z25>,
<26>, <x26>, <y26>, <z26>,
<27>, <x27>, <y27>, <z27>]
<> means optional
beamIntegration commandsÂ¶

beamIntegration
(type, tag, *args)Â¶ A wide range of numerical integration options are available in OpenSees to represent distributed plasticity or nonprismatic section details in BeamColumn Elements, i.e., across the entire element domain [0, L].
Following are beamIntegration types available in the OpenSees:
Integration Methods for Distributed Plasticity. Distributed plasticity methods permit yielding at any integration point along the element length.
 Lobatto
 Legendre
 NewtonCotes
 Radau
 Trapezoidal
 CompositeSimpson
 UserDefined
 FixedLocation
 LowOrder
 MidDistance
LobattoÂ¶

beamIntegration
('Lobatto', tag, secTag, N) Create a GaussLobatto beamIntegration object. GaussLobatto integration is the most common approach for evaluating the response of forceBeamColumnElement (Neuenhofer and Filippou 1997) because it places an integration point at each end of the element, where bending moments are largest in the absence of interior element loads.
tag
(int)tag of the beam integration. secTag
(int)A previousdefined section object. N
(int)Number of integration points along the element.
LegendreÂ¶

beamIntegration
('Legendre', tag, secTag, N) Create a GaussLegendre beamIntegration object. GaussLegendre integration is more accurate than GaussLobatto; however, it is not common in forcebased elements because there are no integration points at the element ends.
Places
N
GaussLegendre integration points along the element. The location and weight of each integration point are tabulated in references on numerical analysis. The force deformation response at each integration point is defined by the section. The order of accuracy for GaussLegendre integration is 2N1.Arguments and examples see Lobatto.
NewtonCotesÂ¶

beamIntegration
('NewtonCotes', tag, secTag, N) Create a NewtonCotes beamIntegration object. NewtonCotes places integration points uniformly along the element, including a point at each end of the element.
Places
N
NewtonCotes integration points along the element. The weights for the uniformly spaced integration points are tabulated in references on numerical analysis. The force deformation response at each integration point is defined by the section. The order of accuracy for GaussRadau integration is N1.Arguments and examples see Lobatto.
RadauÂ¶

beamIntegration
('Radau', tag, secTag, N) Create a GaussRadau beamIntegration object. GaussRadau integration is not common in forcebased elements because it places an integration point at only one end of the element; however, it forms the basis for optimal plastic hinge integration methods.
Places
N
GaussRadau integration points along the element with a point constrained to be at ndI. The location and weight of each integration point are tabulated in references on numerical analysis. The forcedeformation response at each integration point is defined by the section. The order of accuracy for GaussRadau integration is 2N2.Arguments and examples see Lobatto.
TrapezoidalÂ¶

beamIntegration
('Trapezoidal', tag, secTag, N) Create a Trapezoidal beamIntegration object.
Arguments and examples see Lobatto.
CompositeSimpsonÂ¶

beamIntegration
('CompositeSimpson', tag, secTag, N) Create a CompositeSimpson beamIntegration object.
Arguments and examples see Lobatto.
UserDefinedÂ¶

beamIntegration
('UserDefined', tag, N, *secTags, *locs, *wts) Create a UserDefined beamIntegration object. This option allows userspecified locations and weights of the integration points.
tag
(int)tag of the beam integration N
(int)number of integration points along the element. secTags
(list (int))A list previousdefined section objects. locs
(list (float))Locations of integration points along the element. wts
(list (float))weights of integration points. locs = [0.1, 0.3, 0.5, 0.7, 0.9] wts = [0.2, 0.15, 0.3, 0.15, 0.2] secs = [1, 2, 2, 2, 1] beamIntegration('UserDefined',1,len(secs),*secs,*locs,*wts)
Places
N
integration points along the element, which are defined inlocs
on the natural domain [0, 1]. The weight of each integration point is defined in thewts
also on the [0, 1] domain. The forcedeformation response at each integration point is defined by thesecs
. Thelocs
,wts
, andsecs
should be of lengthN
. In general, there is no accuracy for this approach to numerical integration.
FixedLocationÂ¶

beamIntegration
('FixedLocation', tag, N, *secTags, *locs) Create a FixedLocation beamIntegration object. This option allows userspecified locations of the integration points. The associated integration weights are computed by the method of undetermined coefficients (Vandermonde system)
\[\sum^N_{i=1}x_i^{j1}w_i = \int_0^1x^{j1}dx = \frac{1}{j},\qquad (j=1,...,N)\]Note that NewtonCotes integration is recovered when the integration point locations are equally spaced.
tag
(int)tag of the beam integration N
(int)number of integration points along the element. secTags
(list (int))A list previousdefined section objects. locs
(list (float))Locations of integration points along the element. Places
N
integration points along the element, whose locations are defined inlocs
. on the natural domain [0, 1]. The forcedeformation response at each integration point is defined by thesecs
. Both thelocs
andsecs
should be of lengthN
. The order of accuracy for Fixed Location integration is N1.
LowOrderÂ¶

beamIntegration
('LowOrder', tag, N, *secTags, *locs, *wts) Create a LowOrder beamIntegration object. This option is a generalization of the FixedLocation and UserDefined integration approaches and is useful for moving load analysis (Kidarsa, Scott and Higgins 2008). The locations of the integration points are user defined, while a selected number of weights are specified and the remaining weights are computed by the method of undetermined coefficients.
\[\sum_{i=1}^{N_f}x_{fi}^{j1}w_{fi}=\frac{1}{j}\sum_{i=1}^{N_c}x_{ci}^{j1}w_{ci}\]Note that FixedLocation integration is recovered when
Nc
is zero.tag
(int)tag of the beam integration N
(int)number of integration points along the element. secTags
(list (int))A list previousdefined section objects. locs
(list (float))Locations of integration points along the element. wts
(list (float))weights of integration points. locs = [0.0, 0.2, 0.5, 0.8, 1.0] wts = [0.2, 0.2] secs = [1, 2, 2, 2, 1] beamIntegration('LowOrder',1,len(secs),*secs,*locs,*wts)
Places
N
integration points along the element, which are defined inlocs
. on the natural domain [0, 1]. The forcedeformation response at each integration point is defined by thesecs
. Both thelocs
andsecs
should be of lengthN
. Thewts
at userselected integration points are specified on [0, 1], which can be of lengthNc
equals0
up toN
. These specified weights are assigned to the firstNc
entries in thelocs
andsecs
, respectively. The order of accuracy for Low Order integration is NNc1.Note
Nc
is determined from the length of thewts
list. Accordingly, FixedLocation integration is recovered whenwts
is an empty list and UserDefined integration is recovered when thewts
andlocs
lists are of equal length.
MidDistanceÂ¶

beamIntegration
('MidDistance', tag, N, *secTags, *locs) Create a MidDistance beamIntegration object. This option allows userspecified locations of the integration points. The associated integration weights are determined from the midpoints between adjacent integration point locations. \(w_i=(x_{i+1}x_{i1})/2\) for \(i=2...N1\), \(w_1=(x_1+x_2)/2\), and \(w_N=1(x_{N1}+x_N)/2\).
tag
(int)tag of the beam integration N
(int)number of integration points along the element. secTags
(list (int))A list previousdefined section objects. locs
(list (float))Locations of integration points along the element. locs = [0.0, 0.2, 0.5, 0.8, 1.0] secs = [1,2,2,2,1] beamIntegration('MidDistance',1,len(secs),*secs,*locs)
Places
N
integration points along the element, whose locations are defined inlocs
on the natural domain [0, 1]. The forcedeformation response at each integration point is defined by thesecs
. Both thelocs
andsecs
should be of length N. This integration rule can only integrate constant functions exactly since the sum of the integration weights is one.For the
locs
shown above, the associated integration weights will be[0.15, 0.2, 0.3, 0.2, 0.15]
.
Plastic Hinge Integration Methods. Plastic hinge integration methods confine material yielding to regions of the element of specified length while the remainder of the element is linear elastic. A summary of plastic hinge integration methods is found in (Scott and Fenves 2006).
UserHingeÂ¶

beamIntegration
('UserHinge', tag, secETag, npL, *secsLTags, *locsL, *wtsL, npR, *secsRTags, *locsR, *wtsR) Create a UserHinge beamIntegration object.
tag
(int)tag of the beam integration secETag
(int)A previousdefined section objects for nonhinge area. npL
(int)number of integration points along the left hinge. secsLTags
(list (int))A list of previousdefined section objects for left hinge area. locsL
(list (float))A list of locations of integration points for left hinge area. wtsL
(list (float))A list of weights of integration points for left hinge area. npR
(int)number of integration points along the right hinge. secsRTags
(list (int))A list of previousdefined section objects for right hinge area. locsR
(list (float))A list of locations of integration points for right hinge area. wtsR
(list (float))A list of weights of integration points for right hinge area. tag = 1 secE = 5 npL = 2 secsL = [1,2] locsL = [0.1,0.2] wtsL = [0.5,0.5] npR = 2 secsR = [3,4] locsR = [0.8,0.9] wtsR = [0.5,0.5] beamIntegration('UserHinge',tag,secE,npL,*secsL,*locsL,*wtsL,npR,*secsR,*locsR,*wtsR)
HingeMidpointÂ¶

beamIntegration
('HingeMidpoint', tag, secI, lpI, secJ, lpJ, secE) Create a HingeMidpoint beamIntegration object. Midpoint integration over each hinge region is the most accurate onepoint integration rule; however, it does not place integration points at the element ends and there is a small integration error for linear curvature distributions along the element.
tag
(int)tag of the beam integration. secI
(int)A previousdefined section object for hinge at I. lpI
(float)The plastic hinge length at I. secJ
(int)A previousdefined section object for hinge at J. lpJ
(float)The plastic hinge length at J. secE
(int)A previousdefined section object for the element interior. The plastic hinge length at end I (J) is equal to
lpI
(lpJ
) and the associated force deformation response is defined by thesecI
(secJ
). The force deformation response of the element interior is defined by thesecE
. Typically, the interior section is linearelastic, but this is not necessary.lpI = 0.1 lpJ = 0.2 beamIntegration('HingeMidpoint',secI,lpI,secJ,lpJ,secE)
HingeRadauÂ¶

beamIntegration
('HingeRadau', tag, secI, lpI, secJ, lpJ, secE) Create a HingeRadau beamIntegration object. Modified twopoint GaussRadau integration over each hinge region places an integration point at the element ends and at 8/3 the hinge length inside the element. This approach represents linear curvature distributions exactly and the characteristic length for softening plastic hinges is equal to the assumed palstic hinge length.
Arguments and examples see HingeMidpoint.
HingeRadauTwoÂ¶

beamIntegration
('HingeRadauTwo', tag, secI, lpI, secJ, lpJ, secE) Create a HingeRadauTwo beamIntegration object. Twopoint GaussRadau integration over each hinge region places an integration point at the element ends and at 2/3 the hinge length inside the element. This approach represents linear curvature distributions exactly; however, the characteristic length for softening plastic hinges is not equal to the assumed plastic hinge length (equals 1/4 of the plastic hinge length).
Arguments and examples see HingeMidpoint.
HingeEndpointÂ¶

beamIntegration
('HingeEndpoint', tag, secI, lpI, secJ, lpJ, secE) Create a HingeEndpoint beamIntegration object. Endpoint integration over each hinge region moves the integration points to the element ends; however, there is a large integration error for linear curvature distributions along the element.
tag
(int)tag of the beam integration. secI
(int)A previousdefined section object for hinge at I. lpI
(float)The plastic hinge length at I. secJ
(int)A previousdefined section object for hinge at J. lpJ
(float)The plastic hinge length at J. secE
(int)A previousdefined section object for the element interior. Arguments and examples see HingeMidpoint.
uniaxialMaterial commandsÂ¶

uniaxialMaterial
(matType, matTag, *matArgs)Â¶ This command is used to construct a UniaxialMaterial object which represents uniaxial stressstrain (or forcedeformation) relationships.
matType
(str)material type matTag
(int)material tag. matArgs
(list)a list of material arguments, must be preceded with *
.
For example,
matType = 'Steel01'
matTag = 1
matArgs = [Fy, E0, b]
uniaxialMaterial(matType, matTag, *matArgs)
The following contain information about available matType
:
Steel & ReinforcingSteel MaterialsÂ¶
 Steel01
 Steel02
 Steel4
 Hysteretic
 ReinforcingSteel
 Dodd_Restrepo
 RambergOsgoodSteel
 SteelMPF
 Steel01Thermal
Steel01Â¶

uniaxialMaterial
('Steel01', matTag, Fy, E0, b, a1, a2, a3, a4) This command is used to construct a uniaxial bilinear steel material object with kinematic hardening and optional isotropic hardening described by a nonlinear evolution equation (REF: Fedeas).
matTag
(int)integer tag identifying material Fy
(float)yield strength E0
(float)initial elastic tangent b
(float)strainhardening ratio (ratio between postyield tangent and initial elastic tangent) a1
(float)isotropic hardening parameter, increase of compression yield envelope as proportion of yield strength after a plastic strain of \(a_2*(F_y/E_0)\) (optional) a2
(float)isotropic hardening parameter (see explanation under a1
). (optional).a3
(float)isotropic hardening parameter, increase of tension yield envelope as proportion of yield strength after a plastic strain of \(a_4*(F_y/E_0)\). (optional) a4
(float)isotropic hardening parameter (see explanation under a3
). (optional)
Note
If strainhardening ratio is zero and you do not expect softening of your system use BandSPD solver.
Steel02Â¶

uniaxialMaterial
('Steel02', matTag, Fy, E0, b, *params, a1=a2*Fy/E0, a2=1.0, a3=a4*Fy/E0, a4=1.0, sigInit=0.0) This command is used to construct a uniaxial GiuffreMenegottoPinto steel material object with isotropic strain hardening.
matTag
(int)integer tag identifying material Fy
(float)yield strength E0
(float)initial elastic tangent b
(float)strainhardening ratio (ratio between postyield tangent and initial elastic tangent) params
(list (float))parameters to control the transition from elastic to plastic branches. params=[R0,cR1,cR2]
. Recommended values: R0=between 10 and 20, cR1=0.925, cR2=0.15a1
(float)isotropic hardening parameter, increase of compression yield envelope as proportion of yield strength after a plastic strain of \(a_2*(F_y/E_0)\) (optional) a2
(float)isotropic hardening parameter (see explanation under a1
). (optional).a3
(float)isotropic hardening parameter, increase of tension yield envelope as proportion of yield strength after a plastic strain of \(a_4*(F_y/E_0)\). (optional) a4
(float)isotropic hardening parameter (see explanation under a3
). (optional)sigInit
(float)Initial Stress Value (optional, default: 0.0) the strain is calculated from
epsP=sigInit/E
if (sigInit!= 0.0) { double epsInit = sigInit/E; eps = trialStrain+epsInit; } else { eps = trialStrain; }
See also
Steel4Â¶

uniaxialMaterial
('Steel4', matTag, Fy, E0, 'asym', 'kin', b_k, *params, b_kc, R_0c, r_1c, r_2c, 'iso', b_i, rho_i, b_l, R_i, l_yp, b_ic, rho_ic, b_lc, R_ic, 'ult', f_u, R_u, f_uc, R_uc, 'init', sig_init, 'mem', cycNum) This command is used to construct a general uniaxial material with combined kinematic and isotropic hardening and optional nonsymmetric behavior.
matTag
(int)integer tag identifying material Fy
(float)yield strength E0
(float)initial elastic tangent 'kin'
(str)apply kinematic hardening b_k
(float)hardening ratio (E_k/E_0) params
(list (float))control the exponential transition from linear elastic to hardening asymptote params=[R_0,r_1,r_2]
. Recommended values:R_0 = 20, r_1 = 0.90, r_2 = 0.15
'iso'
(str)apply isotropic hardening b_i
(float)initial hardening ratio (E_i/E_0) b_l
(float)saturated hardening ratio (E_is/E_0) rho_i
(float)specifies the position of the intersection point between initial and saturated hardening asymptotes R_i
(float)control the exponential transition from initial to saturated asymptote l_yp
(float)length of the yield plateau in eps_y0 = f_y / E_0 units 'ult'
(str)apply an ultimate strength limit f_u
(float)ultimate strength R_u
(float)control the exponential transition from kinematic hardening to perfectly plastic asymptote 'asym'
(str)assume nonsymmetric behavior 'init'
(str)apply initial stress sig_init
(float)initial stress value 'mem'
(str)configure the load history memory cycNum
(float)expected number of halfcycles during the loading process Efficiency of the material can be slightly increased by correctly setting this value. The default value is cycNum = 50
Load history memory can be turned off by settingcycNum = 0
.
See also
HystereticÂ¶

uniaxialMaterial
('Hysteretic', matTag, *p1, *p2, *p3=p2, *n1, *n2, *n3=n2, pinchX, pinchY, damage1, damage2, beta=0.0) This command is used to construct a uniaxial bilinear hysteretic material object with pinching of force and deformation, damage due to ductility and energy, and degraded unloading stiffness based on ductility.
matTag
(int)integer tag identifying material p1
(list (float))p1=[s1p, e1p]
, stress and strain (or force & deformation) at first point of the envelope in the positive directionp2
(list (float))p2=[s2p, e2p]
, stress and strain (or force & deformation) at second point of the envelope in the positive directionp3
(list (float))p3=[s3p, e3p]
, stress and strain (or force & deformation) at third point of the envelope in the positive directionn1
(list (float))n1=[s1n, e1n]
, stress and strain (or force & deformation) at first point of the envelope in the negative directionn2
(list (float))n2=[s2n, e2n]
, stress and strain (or force & deformation) at second point of the envelope in the negative directionn3
(list (float))n3=[s3n, e3n]
, stress and strain (or force & deformation) at third point of the envelope in the negative directionpinchX
(float)pinching factor for strain (or deformation) during reloading pinchY
(float)pinching factor for stress (or force) during reloading damage1
(float)damage due to ductility: D1(mu1) damage2
(float)damage due to energy: D2(Eii/Eult) beta
(float)power used to determine the degraded unloading stiffness based on ductility, mubeta (optional, default=0.0)
See also
ReinforcingSteelÂ¶

uniaxialMaterial
('ReinforcingSteel', matTag, fy, fu, Es, Esh, eps_sh, eps_ult, 'GABuck', lsr, beta, r, gamma, 'DMBuck', lsr, alpha=1.0, 'CMFatigue', Cf, alpha, Cd, 'IsoHard', a1=4.3, limit=1.0, 'MPCurveParams', R1=0.333, R2=18.0, R3=4.0) This command is used to construct a ReinforcingSteel uniaxial material object. This object is intended to be used in a reinforced concrete fiber section as the steel reinforcing material.
matTag
(int)integer tag identifying material fy
(float)Yield stress in tension fu
(float)Ultimate stress in tension Es
(float)Initial elastic tangent Esh
(float)Tangent at initial strain hardening eps_sh
(float)Strain corresponding to initial strain hardening eps_ult
(float)Strain at peak stress 'GABuck'
(str)Buckling Model Based on Gomes and Appleton (1997) lsr
(float)Slenderness Ratio beta
(float)Amplification factor for the buckled stress strain curve. r
(float)Buckling reduction factor
r can be a real number between [0.0 and 1.0]
r=1.0 full reduction (no buckling)
r=0.0 no reduction
0.0<r<1.0 linear interpolation between buckled and unbuckled curves
gamma
(float)Buckling constant 'DMBuck'
(str)Buckling model based on Dhakal and Maekawa (2002) lsr
(float)Slenderness Ratio alpha
(float)Adjustment Constant usually between 0.75 and 1.0 Default: alpha=1.0, this parameter is optional. 'CMFatigue'
(str)CoffinManson Fatigue and Strength Reduction Cf
(float)CoffinManson constant C alpha
(float)CoffinManson constant a Cd
(float)Cyclic strength reduction constant 'IsoHard'
(str)Isotropic Hardening / Diminishing Yield Plateau a1
(float)Hardening constant (default = 4.3) limit
(float)Limit for the reduction of the yield plateau. % of original plateau length to remain (0.01 < limit < 1.0 ) Limit =1.0, then no reduction takes place (default =0.01) 'MPCurveParams'
(str)Menegotto and Pinto Curve Parameters R1
(float)(default = 0.333) R2
(float)(default = 18) R3
(float)(default = 4)
See also
Dodd_RestrepoÂ¶

uniaxialMaterial
('Dodd_Restrepo', matTag, Fy, Fsu, ESH, ESU, Youngs, ESHI, FSHI, OmegaFac=1.0) This command is used to construct a DoddRestrepo steel material
matTag
(int)integer tag identifying material Fy
(float)Yield strength Fsu
(float)Ultimate tensile strength (UTS) ESH
(float)Tensile strain at initiation of strain hardening ESU
(float)Tensile strain at the UTS Youngs
(float)Modulus of elasticity ESHI
(float)Tensile strain for a point on strain hardening curve, recommended range of values for ESHI: [ (ESU + 5*ESH)/6, (ESU + 3*ESH)/4] FSHI
(float)Tensile stress at point on strain hardening curve corresponding to ESHI OmegaFac
(float)Roundedness factor for Bauschinger curve in cycle reversals from the strain hardening curve. Range: [0.75, 1.15]. Largest value tends to near a bilinear Bauschinger curve. Default = 1.0.
See also
RambergOsgoodSteelÂ¶

uniaxialMaterial
('RambergOsgoodSteel', matTag, fy, E0, a, n) This command is used to construct a RambergOsgood steel material object.
matTag
(int)integer tag identifying material fy
(float)Yield strength E0
(float)initial elastic tangent a
(float)âyield offsetâ and the Commonly used value for a is 0.002 n
(float)Parameters to control the transition from elastic to plastic branches. And controls the hardening of the material by increasing the ânâ hardening ratio will be decreased. Commonly used values for n are ~5 or greater.
See also
SteelMPFÂ¶

uniaxialMaterial
('SteelMPF', matTag, fyp, fyn, E0, bp, bn, *params, a1=0.0, a2=1.0, a3=0.0, a4=1.0) This command is used to construct a uniaxialMaterial SteelMPF (Kolozvari et al., 2015), which represents the wellknown uniaxial constitutive nonlinear hysteretic material model for steel proposed by Menegotto and Pinto (1973), and extended by Filippou et al. (1983) to include isotropic strain hardening effects.
matTag
(int)integer tag identifying material fyp
(float)Yield strength in tension (positive loading direction) fyn
(float)Yield strength in compression (negative loading direction) E0
(float)Initial tangent modulus bp
(float)Strain hardening ratio in tension (positive loading direction) bn
(float)Strain hardening ratio in compression (negative loading direction) params
(list (float))parameters to control the transition from elastic to plastic branches. params=[R0,cR1,cR2]
. Recommended values:R0=20
,cR1=0.925
,cR2=0.15
orcR2=0.0015
a1
(float)Isotropic hardening in compression parameter (optional, default = 0.0). Shifts compression yield envelope by a proportion of compressive yield strength after a maximum plastic tensile strain of a2(fyp/E0) a2
(float)Isotropic hardening in compression parameter (optional, default = 1.0). a3
(float)Isotropic hardening in tension parameter (optional, default = 0.0). Shifts tension yield envelope by a proportion of tensile yield strength after a maximum plastic compressive strain of a3(fyn/E0). a4
(float)Isotropic hardening in tension parameter (optional, default = 1.0). See explanation of a3.
See also
Steel01ThermalÂ¶

uniaxialMaterial
('Steel01Thermal', matTag, Fy, E0, b, a1, a2, a3, a4) This command is the thermal version for
'Steel01'
.matTag
(int)integer tag identifying material Fy
(float)yield strength E0
(float)initial elastic tangent b
(float)strainhardening ratio (ratio between postyield tangent and initial elastic tangent) a1
(float)isotropic hardening parameter, increase of compression yield envelope as proportion of yield strength after a plastic strain of \(a_2*(F_y/E_0)\) (optional) a2
(float)isotropic hardening parameter (see explanation under a1
). (optional).a3
(float)isotropic hardening parameter, increase of tension yield envelope as proportion of yield strength after a plastic strain of \(a_4*(F_y/E_0)\). (optional) a4
(float)isotropic hardening parameter (see explanation under a3
). (optional)
Concrete MaterialsÂ¶
 Concrete01
 Concrete02
 Concrete04
 Concrete06
 Concrete07
 Concrete01WithSITC
 ConfinedConcrete01
 ConcreteD
 FRPConfinedConcrete
 FRPConfinedConcrete02
 ConcreteCM
 TDConcrete
 TDConcreteEXP
 TDConcreteMC10
 TDConcreteMC10NL
Concrete01Â¶

uniaxialMaterial
('Concrete01', matTag, fpc, epsc0, fpcu, epsU) This command is used to construct a uniaxial KentScottPark concrete material object with degraded linear unloading/reloading stiffness according to the work of KarsanJirsa and no tensile strength. (REF: Fedeas).
matTag
(int)integer tag identifying material fpc
(float)concrete compressive strength at 28 days (compression is negative) epsc0
(float)concrete strain at maximum strength fpcu
(float)concrete crushing strength epsU
(float)concrete strain at crushing strength
Note
 Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
 The initial slope for this model is (2*fpc/epsc0)
See also
Concrete02Â¶

uniaxialMaterial
('Concrete02', matTag, fpc, epsc0, fpcu, epsU, lambda, ft, Ets) This command is used to construct a uniaxial KentScottPark concrete material object with degraded linear unloading/reloading stiffness according to the work of KarsanJirsa and no tensile strength. (REF: Fedeas).
matTag
(int)integer tag identifying material fpc
(float)concrete compressive strength at 28 days (compression is negative) epsc0
(float)concrete strain at maximum strength fpcu
(float)concrete crushing strength epsU
(float)concrete strain at crushing strength lambda
(float)ratio between unloading slope at $epscu and initial slope ft
(float)tensile strength Ets
(float)tension softening stiffness (absolute value) (slope of the linear tension softening branch)
Note
 Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
 The initial slope for this model is (2*fpc/epsc0)
See also
Concrete04Â¶

uniaxialMaterial
('Concrete04', matTag, fc, epsc, epscu, Ec, fct, et, beta) This command is used to construct a uniaxial Popovics concrete material object with degraded linear unloading/reloading stiffness according to the work of KarsanJirsa and tensile strength with exponential decay.
matTag
(int)integer tag identifying material fc
(float)floating point values defining concrete compressive strength at 28 days (compression is negative) epsc
(float)floating point values defining concrete strain at maximum strength epscu
(float)floating point values defining concrete strain at crushing strength Ec
(float)floating point values defining initial stiffness fct
(float)floating point value defining the maximum tensile strength of concrete (optional) et
(float)floating point value defining ultimate tensile strain of concrete (optional) beta
(float)loating point value defining the exponential curve parameter to define the residual stress (as a factor of ft) at etu
Note
 Compressive concrete parameters should be input as negative values.
 The envelope of the compressive stressstrain response is defined using the model proposed by Popovics (1973). If the user defines \(Ec = 57000*sqrt(fcc)\) (in psi)â then the envelope curve is identical to proposed by Mander et al. (1988).
 Model Characteristic: For loading in compression, the envelope to the stressstrain curve follows the model proposed by Popovics (1973) until the concrete crushing strength is achieved and also for strains beyond that corresponding to the crushing strength. For unloading and reloading in compression, the KarsanJirsa model (1969) is used to determine the slope of the curve. For tensile loading, an exponential curve is used to define the envelope to the stressstrain curve. For unloading and reloading in tensile, the secant stiffness is used to define the path.
See also
Concrete06Â¶

uniaxialMaterial
('Concrete06', matTag, fc, e0, n, k, alpha1, fcr, ecr, b, alpha2) This command is used to construct a uniaxial concrete material object with tensile strength, nonlinear tension stiffening and compressive behavior based on Thorenfeldt curve.
matTag
(int)integer tag identifying material fc
(float)concrete compressive strength (compression is negative) e0
(float)strain at compressive strength n
(float)compressive shape factor k
(float)postpeak compressive shape factor alpha1
(float)\(\alpha_1\) parameter for compressive plastic strain definition fcr
(float)tensile strength ecr
(float)tensile strain at peak stress (fcr) b
(float)exponent of the tension stiffening curve alpha2
(float)\(\alpha_2\) parameter for tensile plastic strain definition
Note
 Compressive concrete parameters should be input as negative values.
See also
Concrete07Â¶

uniaxialMaterial
('Concrete07', matTag, fc, epsc, Ec, ft, et, xp, xn, r) Concrete07 is an implementation of Chang & Manderâs 1994 concrete model with simplified unloading and reloading curves. Additionally the tension envelope shift with respect to the origin proposed by Chang and Mander has been removed. The model requires eight input parameters to define the monotonic envelope of confined and unconfined concrete in the following form:
matTag
(int)integer tag identifying material fc
(float)concrete compressive strength (compression is negative) epsc
(float)concrete strain at maximum compressive strength Ec
(float)Initial Elastic modulus of the concrete ft
(float)tensile strength of concrete (tension is positive) et
(float)tensile strain at max tensile strength of concrete xp
(float)Nondimensional term that defines the strain at which the straight line descent begins in tension xn
(float)Nondimensional term that defines the strain at which the straight line descent begins in compression r
(float)Parameter that controls the nonlinear descending branch
See also
Concrete01WithSITCÂ¶

uniaxialMaterial
('Concrete01WithSITC', matTag, fpc, epsc0, fpcu, epsU, endStrainSITC=0.01) This command is used to construct a modified uniaxial KentScottPark concrete material object with degraded linear unloading/reloading stiffness according to the work of KarsanJirsa and no tensile strength. The modification is to model the effect of Stuff In The Cracks (SITC).
matTag
(int)integer tag identifying material fpc
(float)concrete compressive strength at 28 days (compression is negative) epsc0
(float)concrete strain at maximum strength fpcu
(float)concrete crushing strength epsU
(float)concrete strain at crushing strength endStrainSITC
(float)optional, default = 0.03
Note
 Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
 The initial slope for this model is (2*fpc/epsc0)
See also
ConfinedConcrete01Â¶

uniaxialMaterial
('ConfinedConcrete01', matTag, secType, fpc, Ec, epscu_type, epscu_val, nu, L1, L2, L3, phis, S, fyh, Es0, haRatio, mu, phiLon, 'internal', *internalArgs, 'wrap', *wrapArgs, 'gravel', 'silica', 'tol', tol, 'maxNumIter', maxNumIter, 'epscuLimit', epscuLimit, 'stRatio', stRatio)
See also
ConcreteDÂ¶

uniaxialMaterial
('ConcreteD', matTag, fc, epsc, ft, epst, Ec, alphac, alphat, cesp=0.25, etap=1.15) This command is used to construct a concrete material based on the Chinese design code.
matTag
(int)integer tag identifying material fc
(float)concrete compressive strength epsc
(float)concrete strain at corresponding to compressive strength ft
(float)concrete tensile strength epst
(float)concrete strain at corresponding to tensile strength Ec
(float)concrete initial Elastic modulus alphac
(float)compressive descending parameter alphat
(float)tensile descending parameter cesp
(float)plastic parameter, recommended values: 0.2~0.3 etap
(float)plastic parameter, recommended values: 1.0~1.3
Note
 Concrete compressive strength and the corresponding strain should be input as negative values.
 The value
fc/epsc
andft/epst
should be smaller thanEc
.
See also
FRPConfinedConcreteÂ¶

uniaxialMaterial
('FRPConfinedConcrete', matTag, fpc1, fpc2, epsc0, D, c, Ej, Sj, tj, eju, S, fyl, fyh, dlong, dtrans, Es, nu0, k, useBuck) This command is used to construct a uniaxial MegalooikonomouMontiSantini concrete material object with degraded linear unloading/reloading stiffness according to the work of KarsanJirsa and no tensile strength.
matTag
(int)integer tag identifying material fpc1
(float)concrete core compressive strength. fpc2
(float)concrete cover compressive strength. epsc0
(float)strain corresponding to unconfined concrete strength. D
(float)diameter of the circular section. c
(float)dimension of concrete cover (until the outer edge of steel stirrups) Ej
(float)elastic modulus of the fiber reinforced polymer (FRP) jacket. Sj
(float)clear spacing of the FRP strips  zero if FRP jacket is continuous. tj
(float)total thickness of the FRP jacket. eju
(float)rupture strain of the FRP jacket from tensile coupons. S
(float)spacing of the steel spiral/stirrups. fyl
(float)yielding strength of longitudinal steel bars. fyh
(float)yielding strength of the steel spiral/stirrups. dlong
(float)diameter of the longitudinal bars of the circular section. dtrans
(float)diameter of the steel spiral/stirrups. Es
(float)elastic modulus of steel. nu0
(float)initial Poissonâs coefficient for concrete. k
(float)reduction factor for the rupture strain of the FRP jacket, recommended values 0.50.8. useBuck
(float)FRP jacket failure criterion due to buckling of longitudinal compressive steel bars (0 = not include it, 1= to include it).
Note
#.IMPORTANT: The units of the input parameters should be in MPa, N, mm. #.Concrete compressive strengths and the corresponding strain should be input as positive values. #.When rupture of FRP jacket occurs due to dilation of concrete (lateral concrete strain exceeding reduced rupture strain of FRP jacket), the analysis is not terminated. Only a message âFRP Ruptureâ is plotted on the screen. #.When $useBuck input parameter is on (equal to 1) and the modelâs longitudinal steel buckling conditions are fulfilled, a message âInitiation of Buckling of Long.Bar under Compressionâ is plotted on the screen. #.When rupture of FRP jacket occurs due to its interaction with buckled longitudinal compressive steel bars, the analysis is not terminated. Only a message âFRP Rupture due to Buckling of Long.Bar under compressionâ is plotted on the screen.
See also
FRPConfinedConcrete02Â¶

uniaxialMaterial
('FRPConfinedConcrete02', matTag, fc0, Ec, ec0, <'JacketC', tfrp, Efrp, erup, R>, <'Ultimate', fcu, ecu>, ft, Ets, Unit) Figure 1 Hysteretic StressStrain Relation
This command is used to construct a uniaxial hysteretic stressstrain model for fiberreinforced polymer (FRP)confined concrete. The envelope compressive stressstrain response is described by a parabolic first portion and a linear second portion with smooth connection between them (Figure 1). The hysteretic rules of compression are based on Lam and Tengâs (2009) model. The cyclic linear tension model of Yassin (1994) for unconfined concrete (as adopted in Concrete02) is used with slight modifications to describe the tensile behavior of FRPconfined concrete (Teng et al. 2015).
matTag
(int)integer tag identifying material fc0
(float)compressive strength of unconfined concrete (compression is negative) Ec
(float)elastic modulus of unconfined concrete (=4730â($fc0(MPa))) ec0
(float)axial strain corresponding to unconfined concrete strength (â 0.002) JacketC
(str)input parameters of the FRP jacket in a circular section tfrp
(float)thickness of an FRP jacket Efrp
(float)tensile elastic modulus of an FRP jacket erup
(float)hoop rupture strain of an FRP jacket R
(float)radius of circular column section Ultimate
(str)input ultimate stress/strain directly fcu
(float)ultimate stress of FRPconfined concrete ($fcu â„ $fc0) ecu
(float)ultimate strain of FRPconfined concrete ft
(float)tensile strength of unconfined concrete (=0.632â($fc0(MPa))) Ets
(float)stiffness of tensile softening (â 0.05 Ec) Unit
(float)unit indicator, Unit = 1 for SI Metric Units; Unit = 0 for US Customary Units
Note
 Compressive concrete parameters should be input as negative values.
 The users are required to input either the FRP jacket properties in an FRPconfined circular column (<JacketC>) or directly input the ultimate point (Î”cu, fcu) (<Ultimate>). If <JacketC> is used, the ultimate stress and strain are automatically calculated based on Teng et al.âs (2009) model which is a refined version of Lam and Tengâs (2003) stressstrain model for FRPconfined concrete in circular columns. If <Ultimate> is used, the ultimate stress and strain can be calculated by the users in advance based on other stressstrain models of FRPconfined concrete and thus can be used for other cross section shapes (e.g., square, rectangular, or elliptical). If none of them is specified, a stressstrain curve (parabola + horizontal linear curve) for unconfined concrete will be defined (Figure 1). Both <JacketC> and <Ultimate> adopt the envelope compressive stressstrain curve with a parabolic first portion and a linear second portion.
 Unit indicator: $Unit = 1 for SI Metric Units (e.g., N, mm, MPa); $Unit = 0 for US Customary Units (e.g., kip, in, sec, ksi).
Calibration:
 The implemented new material has been calibrated using a simplesupported ForceBased BeamColumn element subjected to axial load only (http://opensees.berkeley.edu/wiki/index.php/Calibration_of_Maxwell_Material). The output stressstrain responses were compared with the desired curves defined by the input parameters.
Examples:
Example 1: Pinended FRPconfined reinforced concrete (RC) columns
Figure 2 Simulation of pinended FRPconfined RC column
The first example is a pinended FRPconfined circular RC column subjected to eccentric compression (load eccentricity = 20 mm) at both ends tested by Bisby and Ranger (2010) (Figure 2). Due to the symmetry in geometry and loading, only half of the column needs to be modelled. In this case, three forceBeamColumn elements each with 5 integration points were used for the half column. The FRPConfinedConcrete02 model was used to describe the stressstrain behavior of FRPconfined concrete. Either <JacketC> or <Ultimate> can be used. If the former is used, the properties of the FRP jacket need to be input; if the latter is used, the ultimate stress and strain need to be calculated by the users and input directly. The eccentric loading is applied with a combined axial load and bending moment at each end node. An increasing vertical displacement is applied to the top node of the column model. The analysis terminated until the ultimate axial strain of FRPconfined concrete was reached by the extreme compression concrete fiber at the midheight (equivalent to FRP rupture). SI Metric Unit (e.g., N, mm, MPa) is used in the script of this example ($Unit = 1).
Figure 3 shows the comparison of axial loadlateral displacement curve between the test results and the theoretical results. Figure 4 shows the variation of column slenderness ratio (l/D) on the axial loadlateral displacement response of the column. Please refer to Lin (2016) for more details about the modeling.
Figure 3 Experimental results vs theoretical results
Figure 4 Parametric study (effect of column slenderness ratio)
Example 2: Cantilever column subjected to constant axial compression and cyclic lateral loading
Figure 5 Simulation of columns under cyclic latera loading
 The second example is a cantilever FRPconfined circular RC column subjected to constant axial compression and cyclic lateral loading (Column C5 tested by Saadatmanesh et al. 1997). The US Customary Units (e.g., kip, in, sec, ksi) were used in this example. The twentyfive (25)in.height region (potential plastic hinge region) above the footing of the column was wrapped with an FRP jacket; the remaining portion of the column with a height of 71 in. was conventional RC section without FRP jacketing. The column was modelled using two forceBeamColumn elements to cater for the variation of section characteristic along the column height. A zero length section element at the columnfooting interface was used to simulate fixedend rotations due to the strain penetration of longitudinal steel bars (Figure 5) (Lin et al. 2012). The bondslip model of Zhao and Sritharan (2007) (Bond_SP01) was used to depict the bar stressslip response. In addition, another zero length section element was used at the columnfooting interface to consider the possible rotations of the footing (Teng et al. 2015). The rotation stiffness of the zero length section element was adjusted to achieve close matching between the test response and the predicted response during the initial stage of loading. This zero length section element was found to have little effect on the ultimate displacement of the column (Teng et al. 2015). Moreover, the inclination of axial load in the column test needs to be accounted for when comparing predicted results with test results (Teng et al. 2015). Figure 6 shows the comparison of lateral loadlateral displacement curve between the test results and the theoretical results.
References:
 Bisby, L. and Ranger, M. (2010). âAxialflexural interaction in circular FRPconfined reinforced concrete columnsâ, Construction and Building Materials, Vol. 24, No. 9, pp. 16721681.
 Lam, L. and Teng, J.G. (2003). âDesignoriented stressstrain model for FRPconfined concreteâ, Construction and Building Materials, Vol. 17, No. 6, pp. 471489.
 Lam, L. and Teng, J.G. (2009). âStressstrain model for FRPconfined concrete under cyclic axial compressionâ, Engineering Structures, Vol. 31, No. 2, pp. 308321.
 Lin, G. (2016). Seismic Performance of FRPconfined RC Columns: StressStrain Models and Numerical Simulation, Ph.D. thesis, Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China.
 Lin, G. and Teng, J.G. (2015). âNumerical simulation of cyclic/seismic lateral response of square RC columns confined with fibrereinforced polymer jacketsâ, Proceedings, Second International Conference on Performancebased and Lifecycle Structural Engineering (PLSE 2015), pp. 481489 (http://plse2015.org/cms/USB/pdf/fullpaper_7408.pdf).
 Lin, G., Teng, J.G. and Lam, L. (2012). âNumerical simulation of FRPjacketed RC columns under cyclic loading: modeling of the strain penetration effectâ, First International Conference on Performancebased and Lifecycle Structural Engineering (PLSE2012), December 57, Hong Kong, China.
 Saadatmanesh, H., Ehsani, M. and Jin, L. (1997). âSeismic retrofitting of rectangular bridge columns with composite strapsâ, Earthquake Spectra, Vol. 13, No. 2, pp. 281304.
 Teng, J.G., Lam, L., Lin, G., Lu, J.Y. and Xiao, Q.G. (2015). âNumerical Simulation of FRPJacketed RC Columns Subjected to Cyclic and Seismic Loadingâ, Journal of Composites for Construction, ASCE, Vol. 20, No. 1, pp. 04015021.
 Yassin, M.H.M. (1994). Nonlinear Analysis of Prestressed Concrete Structures under Monotonic and Cyclic Loads, Ph.D. thesis, University of California at Berkeley, California, USA.
 Zhao, J. and Sritharan, S. (2007). âModeling of strain penetration effects in fiberbased analysis of reinforced concrete structuresconcrete structuresâ, ACI Structural Journal, Vol. 104, No. 2, pp. 133141.
ConcreteCMÂ¶

uniaxialMaterial
('ConcreteCM', matTag, fpcc, epcc, Ec, rc, xcrn, ft, et, rt, xcrp, 'GapClose', GapClose=0) This command is used to construct a uniaxialMaterial ConcreteCM (Kolozvari et al., 2015), which is a uniaxial hysteretic constitutive model for concrete developed by Chang and Mander (1994).
matTag
(int)integer tag identifying material fpcc
(float)Compressive strength (\(f'_c\)) epcc
(float)Strain at compressive strength (\(\epsilon'_c\)) Ec
(float)Initial tangent modulus (\(E_c\)) rc
(float)Shape parameter in Tsaiâs equation defined for compression (\(r_c\)) xcrn
(float)Nondimensional critical strain on compression envelope (\(\epsilon^{}_{cr}\), where the envelope curve starts following a straight line) ft
(float)Tensile strength (\(f_t\)) et
(float)Strain at tensile strength (\(\epsilon_t\)) rt
(float)Shape parameter in Tsaiâs equation defined for tension (\(r_t\)) xcrp
(float)Nondimensional critical strain on tension envelope (\(\epsilon^{+}_{cr}\), where the envelope curve starts following a straight line  large value [e.g., 10000] recommended when tension stiffening is considered) GapClose
(float)GapClose = 0, less gradual gap closure (default); GapClose = 1, more gradual gap closure
See also
TDConcreteÂ¶

uniaxialMaterial
('TDConcrete', matTag, fc, fct, Ec, beta, tD, epsshu, psish, Tcr, phiu, psicr1, psicr2, tcast) This command is used to construct a uniaxial timedependent concrete material object with linear behavior in compression, nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to ACI 209R92.
matTag
(int)integer tag identifying material fc
(float)concrete compressive strength (compression is negative) fct
(float)concrete tensile strength (tension is positive) Ec
(float)concrete modulus of elasticity beta
(float)tension softening parameter (tension softening exponent) tD
(float)analysis time at initiation of drying (in days) epsshu
(float)ultimate shrinkage strain as per ACI 209R92 (shrinkage is negative) psish
(float)fitting parameter of the shrinkage time evolution function as per ACI 209R92 Tcr
(float)creep model age (in days) phiu
(float)ultimate creep coefficient as per ACI 209R92 psicr1
(float)fitting parameter of the creep time evolution function as per ACI 209R92 psicr2
(float)fitting parameter of the creep time evolution function as per ACI 209R92 tcast
(float)analysis time corresponding to concrete casting (in days; minimum value 2.0)
Note
 Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
 Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
See also
Detailed descriptions of the model and its implementation can be found in the following: (1) Knaack, A.M., Kurama, Y.C. 2018. Modeling TimeDependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175190. doi:10.14359/51701153 (2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: shortterm and longterm behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp A manual describing the use of the model and sample files can be found at: https://data.mendeley.com/datasets/z4gxnhchky/1
TDConcreteEXPÂ¶

uniaxialMaterial
('TDConcreteEXP', matTag, fc, fct, Ec, beta, tD, epsshu, psish, Tcr, epscru, sigCr, psicr1, psicr2, tcast) This command is used to construct a uniaxial timedependent concrete material object with linear behavior in compression, nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to ACI 209R92.
matTag
(int)integer tag identifying material fc
(float)concrete compressive strength (compression is negative) fct
(float)concrete tensile strength (tension is positive) Ec
(float)concrete modulus of elasticity beta
(float)tension softening parameter (tension softening exponent) tD
(float)analysis time at initiation of drying (in days) epsshu
(float)ultimate shrinkage strain as per ACI 209R92 (shrinkage is negative) psish
(float)fitting parameter of the shrinkage time evolution function as per ACI 209R92 Tcr
(float)creep model age (in days) epscru
(float)ultimate creep strain (e.g., taken from experimental measurements) sigCr
(float)concrete compressive stress (input as negative) associated with $epscru (e.g., experimentally applied) psicr1
(float)fitting parameter of the creep time evolution function as per ACI 209R92 psicr2
(float)fitting parameter of the creep time evolution function as per ACI 209R92 tcast
(float)analysis time corresponding to concrete casting (in days; minimum value 2.0)
Note
 Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
 Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
See also
Detailed descriptions of the model and its implementation can be found in the following: (1) Knaack, A.M., Kurama, Y.C. 2018. Modeling TimeDependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175190. doi:10.14359/51701153 (2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: shortterm and longterm behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp A manual describing the use of the model and sample files can be found at: https://data.mendeley.com/datasets/z4gxnhchky/1
TDConcreteMC10Â¶

uniaxialMaterial
('TDConcreteMC10', matTag, fc, fct, Ec, Ecm, beta, tD, epsba, epsbb, epsda, epsdb, phiba, phibb, phida, phidb, tcast, cem) This command is used to construct a uniaxial timedependent concrete material object with linear behavior in compression, nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to fib Model Code 2010.
matTag
(int)integer tag identifying material fc
(float)concrete compressive strength (compression is negative) fct
(float)concrete tensile strength (tension is positive) Ec
(float)concrete modulus of elasticity at loading age Ecm
(float)concrete modulus of elasticity at 28 days beta
(float)tension softening parameter (tension softening exponent) tD
(float)analysis time at initiation of drying (in days) epsba
(float)ultimate basic shrinkage strain (input as negative) as per fib Model Code 2010 epsbb
(float)fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010 epsda
(float)product of ultimate drying shrinkage strain and relative humidity function as per fib Model Code 2010 epsdb
(float)fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010 phiba
(float)parameter for the effect of compressive strength on basic creep as per fib Model Code 2010 phibb
(float)fitting parameter of the basic creep time evolution function as per fib Model Code 2010 phida
(float)product of the effect of compressive strength and relative humidity on drying creep as per fib Model Code 2010 phidb
(float)fitting parameter of the drying creep time evolution function as per fib Model Code 2010 tcast
(float)analysis time corresponding to concrete casting (in days; minimum value 2.0) cem
(float)coefficient dependent on the type of cement as per fib Model Code 2010
Note
 Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
 Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
See also
Detailed descriptions of the model and its implementation can be found in the following: (1) Knaack, A.M., Kurama, Y.C. 2018. Modeling TimeDependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175190. doi:10.14359/51701153 (2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: shortterm and longterm behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp A manual describing the use of the model and sample files can be found at: https://data.mendeley.com/datasets/z4gxnhchky/1
TDConcreteMC10NLÂ¶

uniaxialMaterial
('TDConcreteMC10NL', matTag, fc, fcu, epscu, fct, Ec, Ecm, beta, tD, epsba, epsbb, epsda, epsdb, phiba, phibb, phida, phidb, tcast, cem) This command is used to construct a uniaxial timedependent concrete material object with nonlinear behavior in compression (REF: Concrete02), nonlinear behavior in tension (REF: Tamai et al., 1988) and creep and shrinkage according to fib Model Code 2010.
matTag
(int)integer tag identifying material fc
(float)concrete compressive strength (compression is negative) fcu
(float)concrete crushing strength (compression is negative) epscu
(float)concrete strain at crushing strength (input as negative) fct
(float)concrete tensile strength (tension is positive) Ec
(float)concrete modulus of elasticity at loading age Ecm
(float)concrete modulus of elasticity at 28 days beta
(float)tension softening parameter (tension softening exponent) tD
(float)analysis time at initiation of drying (in days) epsba
(float)ultimate basic shrinkage strain (input as negative) as per fib Model Code 2010 epsbb
(float)fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010 epsda
(float)product of ultimate drying shrinkage strain and relative humidity function as per fib Model Code 2010 epsdb
(float)fitting parameter of the basic shrinkage time evolution function as per fib Model Code 2010 phiba
(float)parameter for the effect of compressive strength on basic creep as per fib Model Code 2010 phibb
(float)fitting parameter of the basic creep time evolution function as per fib Model Code 2010 phida
(float)product of the effect of compressive strength and relative humidity on drying creep as per fib Model Code 2010 phidb
(float)fitting parameter of the drying creep time evolution function as per fib Model Code 2010 tcast
(float)analysis time corresponding to concrete casting (in days; minimum value 2.0) cem
(float)coefficient dependent on the type of cement as per fib Model Code 2010
Note
 Compressive concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
 Shrinkage concrete parameters should be input as negative values (if input as positive, they will be converted to negative internally).
See also
Detailed descriptions of the model and its implementation can be found in the following: (1) Knaack, A.M., Kurama, Y.C. 2018. Modeling TimeDependent Deformations: Application for Reinforced Concrete Beams with Recycled Concrete Aggregates. ACI Structural J. 115, 175190. doi:10.14359/51701153 (2) Knaack, A.M., 2013. Sustainable concrete structures using recycled concrete aggregate: shortterm and longterm behavior considering material variability. PhD Dissertation, Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, Indiana, USA, 680 pp A manual describing the use of the model and sample files can be found at: https://data.mendeley.com/datasets/z4gxnhchky/1
Standard Uniaxial MaterialsÂ¶
 Elastic Uniaxial Material
 ElasticPerfectly Plastic Material
 ElasticPerfectly Plastic Gap Material
 ElasticNo Tension Material
 Parallel Material
 Series Material
Elastic Uniaxial MaterialÂ¶

uniaxialMaterial
('Elastic', matTag, E, eta=0.0, Eneg=E) This command is used to construct an elastic uniaxial material object.
matTag
(int)integer tag identifying material E
(float)tangent eta
(float)damping tangent (optional, default=0.0) Eneg
(float)tangent in compression (optional, default=E)
See also
ElasticPerfectly Plastic MaterialÂ¶

uniaxialMaterial
('ElasticPP', matTag, E, epsyP, epsyN=epsyP, eps0=0.0) This command is used to construct an elastic perfectlyplastic uniaxial material object.
matTag
(int)integer tag identifying material E
(float)tangent epsyP
(float)strain or deformation at which material reaches plastic state in tension epsyN
(float)strain or deformation at which material reaches plastic state in compression. (optional, default is tension value) eps0
(float)initial strain (optional, default: zero)
See also
ElasticPerfectly Plastic Gap MaterialÂ¶

uniaxialMaterial
('ElasticPPGap', matTag, E, Fy, gap, eta=0.0, damage='noDamage') This command is used to construct an elastic perfectlyplastic gap uniaxial material object.
matTag
(int)integer tag identifying material E
(float)tangent Fy
(float)stress or force at which material reaches plastic state gap
(float)initial gap (strain or deformation) eta
(float)hardening ratio (=Eh/E), which can be negative damage
(str)an optional string to specify whether to accumulate damage or not in the material. With the default string, 'noDamage'
the gap material will recenter on load reversal. If the string'damage'
is provided this recentering will not occur and gap will grow.
See also
ElasticNo Tension MaterialÂ¶

uniaxialMaterial
('ENT', matTag, E) This command is used to construct a uniaxial elasticno tension material object.
matTag
(int)integer tag identifying material E
(float)tangent
See also
Parallel MaterialÂ¶

uniaxialMaterial
('Parallel', matTag, *MatTags, 'factors', *factorArgs) This command is used to construct a parallel material object made up of an arbitrary number of previouslyconstructed UniaxialMaterial objects.
matTag
(int)integer tag identifying material MatTags
(list (int))identification tags of materials making up the material model factorArgs
(list (float))factors to create a linear combination of the specified materials. Factors can be negative to subtract one material from an other. (optional, default = 1.0)
See also
Series MaterialÂ¶

uniaxialMaterial
('Series', matTag, *matTags) This command is used to construct a series material object made up of an arbitrary number of previouslyconstructed UniaxialMaterial objects.
matTag
(int)integer tag identifying material matTags
(list (int))identification tags of materials making up the material model
See also
PyTzQz uniaxial materials for py, tz and qz elements for modeling soilstructure interaction through the piles in a structural foundationÂ¶
PySimple1 MaterialÂ¶

uniaxialMaterial
('PySimple1', matTag, soilType, pult, Y50, Cd, c=0.0) This command is used to construct a PySimple1 uniaxial material object.
matTag
(int)integer tag identifying material soilType
(int)soilType = 1 Backbone of py curve approximates Matlock (1970) soft clay relation.
soilType = 2 Backbone of py curve approximates API (1993) sand relation.
pult
(float)Ultimate capacity of the py material. Note that âpâ or âpultâ are distributed loads [force per length of pile] in common design equations, but are both loads for this uniaxialMaterial [i.e., distributed load times the tributary length of the pile]. Y50
(float)Displacement at which 50% of pult is mobilized in monotonic loading. Cd
(float)Variable that sets the drag resistance within a fullymobilized gap as Cd*pult. c
(float)The viscous damping term (dashpot) on the farfield (elastic) component of the displacement rate (velocity). (optional Default = 0.0). Nonzero c values are used to represent radiation damping effects
See also
TzSimple1 MaterialÂ¶

uniaxialMaterial
('TzSimple1', matTag, soilType, tult, z50, c=0.0) This command is used to construct a TzSimple1 uniaxial material object.
matTag
(int)integer tag identifying material soilType
(int)soilType = 1 Backbone of tz curve approximates Reese and OâNeill (1987).
soilType = 2 Backbone of tz curve approximates Mosher (1984) relation.
tult
(float)Ultimate capacity of the tz material. SEE NOTE 1. z50
(float)Displacement at which 50% of tult is mobilized in monotonic loading. c
(float)The viscous damping term (dashpot) on the farfield (elastic) component of the displacement rate (velocity). (optional Default = 0.0). See NOTE 2.
Note
 The argument tult is the ultimate capacity of the tz material. Note that âtâ or âtultâ are shear stresses [force per unit area of pile surface] in common design equations, but are both loads for this uniaxialMaterial [i.e., shear stress times the tributary area of the pile].
 Nonzero c values are used to represent radiation damping effects
See also
QzSimple1 MaterialÂ¶

uniaxialMaterial
('QzSimple1', matTag, qzType, qult, Z50, suction=0.0, c=0.0) This command is used to construct a QzSimple1 uniaxial material object.
matTag
(int)integer tag identifying material qzType
(int)qzType = 1 Backbone of qz curve approximates Reese and OâNeillâs (1987) relation for drilled shafts in clay.
qzType = 2 Backbone of qz curve approximates Vijayvergiyaâs (1977) relation for piles in sand.
qult
(float)Ultimate capacity of the qz material. SEE NOTE 1. Z50
(float)Displacement at which 50% of qult is mobilized in monotonic loading. SEE NOTE 2. suction
(float)Uplift resistance is equal to suction*qult. Default = 0.0. The value of suction must be 0.0 to 0.1.* c
(float)The viscous damping term (dashpot) on the farfield (elastic) component of the displacement rate (velocity). Default = 0.0. Nonzero c values are used to represent radiation damping effects.*
Note
qult
: Ultimate capacity of the qz material. Note thatq1
orqult
are stresses [force per unit area of pile tip] in common design equations, but are both loads for this uniaxialMaterial [i.e., stress times tip area].Y50
: Displacement at which 50% of pult is mobilized in monotonic loading. Note that Vijayvergiyaâs relation (qzType=2) refers to a âcriticalâ displacement (zcrit) at which qult is fully mobilized, and that the corresponding z50 would be 0. 125zcrit. optional args
suction
andc
must either both be omitted or both provided.
See also
PyLiq1 MaterialÂ¶

uniaxialMaterial
('PyLiq1', matTag, soilType, pult, Y50, Cd, c, pRes, ele1, ele2)

uniaxialMaterial
('PyLiq1', matTag, soilType, pult, Y50, Cd, c, pRes, 'timeSeries', timeSeriesTag) This command constructs a uniaxial py material that incorporates liquefaction effects. This p y material is used with a zeroLength element to connect a pile (beamcolumn element) to a 2 D planestrain FE mesh or displacement boundary condition. The py material obtains the average mean effective stress (which decreases with increasing excess pore pressure) either from two specified soil elements, or from a time series. Currently, the implementation requires that the specified soil elements consist of FluidSolidPorousMaterials in FourNodeQuad elements, or PressureDependMultiYield or PressureDependMultiYield02 materials in FourNodeQuadUP or NineFourQuadUP elements. There are two possible forms:
matTag
(int)integer tag identifying material soilType
(int)soilType = 1 Backbone of py curve approximates Matlock (1970) soft clay relation. soilType = 2 Backbone of py curve approximates API (1993) sand relation. pult
(float)Ultimate capacity of the py material. Note that âpâ or âpultâ are distributed loads [force per length of pile] in common design equations, but are both loads for this uniaxialMaterial [i.e., distributed load times the tributary length of the pile]. Y50
(float)Displacement at which 50% of pult is mobilized in monotonic loading. Cd
(float)Variable that sets the drag resistance within a fullymobilized gap as Cd*pult. c
(float)The viscous damping term (dashpot) on the farfield (elastic) component of the displacement rate (velocity). (optional Default = 0.0). Nonzero c values are used to represent radiation damping effects pRes
(float)sets the minimum (or residual) peak resistance that the material retains as the adjacent solid soil elements liquefy ele1
ele2
(float)are the eleTag (element numbers) for the two solid elements from which PyLiq1 will obtain mean effective stresses and excess pore pressures timeSeriesTag
(float)Alternatively, mean effective stress can be supplied by a time series by specifying the text string 'timeSeries'
and the tag of the seriesseriesTag
.
See also
TzLiq1 MaterialÂ¶

uniaxialMaterial
('TzLiq1', matTag, tzType, tult, z50, c, ele1, ele2)

uniaxialMaterial
('TzLiq1', matTag, tzType, tult, z50, c, 'timeSeries', timeSeriesTag) The command constructs a uniaxial tz material that incorporates liquefaction effects. This t z material is used with a zeroLength element to connect a pile (beamcolumn element) to a 2 D planestrain FE mesh. The tz material obtains the average mean effective stress (which decreases with increasing excess pore pressure) from two specified soil elements. Currently, the implementation requires that the specified soil elements consist of FluidSolidPorousMaterials in FourNodeQuad elements.
matTag
(int)integer tag identifying material tzType
(int)tzType = 1 Backbone of tz curve approximates Reese and OâNeill (1987). tzType = 2 Backbone of tz curve approximates Mosher (1984) relation. tult
(float)Ultimate capacity of the tz material. SEE NOTE 1. z50
(float)Displacement at which 50% of tult is mobilized in monotonic loading. c
(float)The viscous damping term (dashpot) on the farfield (elastic) component of the displacement rate (velocity). ele1
ele2
(float)are the eleTag (element numbers) for the two solid elements from which PyLiq1 will obtain mean effective stresses and excess pore pressures timeSeriesTag
(float)Alternatively, mean effective stress can be supplied by a time series by specifying the text string 'timeSeries'
and the tag of the seriesmseriesTag
.
Note
 The argument
tult
is the ultimate capacity of the tz material. Note that âtâ or âtultâ are shear stresses [force per unit area of pile surface] in common design equations, but are both loads for this uniaxialMaterial [i.e., shear stress times the tributary area of the pile].  Nonzero c values are used to represent radiation damping effects
 To model the effects of liquefaction with
TzLiq1
, it is necessary to use the material stage updating command:
See also
Other Uniaxial MaterialsÂ¶
 Hardening Material
 CastFuse Material
 ViscousDamper Material
 BilinearOilDamper Material
 Modified IbarraMedinaKrawinkler Deterioration Model with Bilinear Hysteretic Response (Bilin Material)
 Modified IbarraMedinaKrawinkler Deterioration Model with PeakOriented Hysteretic Response (ModIMKPeakOriented Material)
 Modified IbarraMedinaKrawinkler Deterioration Model with Pinched Hysteretic Response (ModIMKPinching Material)
 SAWS Material
 BarSlip Material
 Bond SP01   Strain Penetration Model for Fully Anchored Steel Reinforcing Bars
 Fatigue Material
 Impact Material
 Hyperbolic Gap Material
 Limit State Material
 MinMax Material
 ElasticBilin Material
 ElasticMultiLinear Material
 MultiLinear
 Initial Strain Material
 Initial Stress Material
 PathIndependent Material
 Pinching4 Material
 Engineered Cementitious Composites Material
 SelfCentering Material
 Viscous Material
 BoucWen Material
 BWBN Material
 KikuchiAikenHDR Material
 KikuchiAikenLRB Material
 AxialSp Material
 AxialSpHD Material
 Pinching Limit State Material
 CFSWSWP WoodSheathed ColdFormed Steel Shear Wall Panel
 CFSSSWP SteelSheathed Coldformed Steel Shear Wall Panel
Hardening MaterialÂ¶

uniaxialMaterial
('Hardening', matTag, E, sigmaY, H_iso, H_kin, eta=0.0) This command is used to construct a uniaxial material object with combined linear kinematic and isotropic hardening. The model includes optional viscoplasticity using a Perzyna formulation.
matTag
(int)integer tag identifying material E
(float)tangent stiffness sigmaY
(float)yield stress or force H_iso
(float)isotropic hardening Modulus H_kin
(float)kinematic hardening Modulus eta
(float)viscoplastic coefficient (optional, default=0.0)
See also
CastFuse MaterialÂ¶

uniaxialMaterial
('Cast', matTag, n, bo, h, fy, E, L, b, Ro, cR1, cR2, a1=s2*Pp/Kp, a2=1.0, a3=a4*Pp/Kp, a4=1.0) This command is used to construct a parallel material object made up of an arbitrary number of previouslyconstructed UniaxialMaterial objects.
matTag
(int)integer tag identifying material n
(int)Number of yield fingers of the CSFbrace bo
(float)Width of an individual yielding finger at its base of the CSFbrace h
(float)Thickness of an individual yielding finger fy
(float)Yield strength of the steel material of the yielding finger E
(float)Modulus of elasticity of the steel material of the yielding finger L
(float)Height of an individual yielding finger b
(float)Strain hardening ratio Ro
(float)Parameter that controls the Bauschinger effect. Recommended Values for $Ro=between 10 to 30 cR1
(float)Parameter that controls the Bauschinger effect. Recommended Value cR1=0.925 cR2
(float)Parameter that controls the Bauschinger effect. Recommended Value cR2=0.150 a1
(float)isotropic hardening parameter, increase of compression yield envelope as proportion of yield strength after a plastic deformation of a2*(Pp/Kp) a2
(float)isotropic hardening parameter (see explanation under a1). (optional default = 1.0) a3
(float)isotropic hardening parameter, increase of tension yield envelope as proportion of yield strength after a plastic deformation of a4*(Pp/Kp) a4
(float)isotropic hardening parameter (see explanation under a3). (optional default = 1.0)
Gray et al. [1] showed that the monotonic backbone curve of a CSFbrace with known properties (n
, bo
, h
, L
, fy
, E
) after yielding can be expressed as a closeform solution that is given by,
\(P = P_p/\cos(2d/L)\), in which \(d\) is the axial deformation of the brace at increment \(i\) and \(P_p\) is the yield strength of the CSFbrace and is given by the following expression
\(P_p = nb_oh^2f_y/4L\)
The elastic stiffness of the CSFbrace is given by,
\(K_p = nb_oEh^3f_y/6L^3\)
See also
ViscousDamper MaterialÂ¶

uniaxialMaterial
('ViscousDamper', matTag, K_el, Cd, alpha, LGap=0.0, NM=1, RelTol=1e6, AbsTol=1e10, MaxHalf=15) This command is used to construct a ViscousDamper material, which represents the Maxwell Model (linear spring and nonlinear dashpot in series). The ViscousDamper material simulates the hysteretic response of nonlinear viscous dampers. An adaptive iterative algorithm has been implemented and validated to solve numerically the constitutive equations within a nonlinear viscous damper with a highprecision accuracy.
matTag
(int)integer tag identifying material K_el
(float)Elastic stiffness of linear spring to model the axial flexibility of a viscous damper (e.g. combined stiffness of the supporting brace and internal damper portion) Cd
(float)Damping coefficient alpha
(float)Velocity exponent LGap
(float)Gap length to simulate the gap length due to the pin tolerance NM
(int)Employed adaptive numerical algorithm (default value NM = 1; * 1
= DormandPrince54, *2
= 6th order AdamsBashforthMoulton, *3
= modified Rosenbrock Triple)RelTol
(float)Tolerance for absolute relative error control of the adaptive iterative algorithm (default value 10^6) AbsTol
(float)Tolerance for absolute error control of adaptive iterative algorithm (default value 10^10) MaxHalf
(int)Maximum number of substep iterations within an integration step (default value 15)
See also
BilinearOilDamper MaterialÂ¶

uniaxialMaterial
('BilinearOilDamper', matTag, K_el, Cd, Fr=1.0, p=1.0, LGap=0.0, NM=1, RelTol=1e6, AbsTol=1e10, MaxHalf=15) This command is used to construct a BilinearOilDamper material, which simulates the hysteretic response of bilinear oil dampers with relief valve. Two adaptive iterative algorithms have been implemented and validated to solve numerically the constitutive equations within a bilinear oil damper with a highprecision accuracy.
matTag
(int)integer tag identifying material K_el
(float)Elastic stiffness of linear spring to model the axial flexibility of a viscous damper (e.g. combined stiffness of the supporting brace and internal damper portion) Cd
(float)Damping coefficient Fr
(float)Damper relief load (default=1.0, Damper property) p
(float)Postrelief viscous damping coefficient ratio (default=1.0, linear oil damper) LGap
(float)Gap length to simulate the gap length due to the pin tolerance NM
(int)Employed adaptive numerical algorithm (default value NM = 1;
1
= DormandPrince54,2
= 6th order AdamsBashforthMoulton,3
= modified Rosenbrock Triple)
RelTol
(float)Tolerance for absolute relative error control of the adaptive iterative algorithm (default value 10^6) AbsTol
(float)Tolerance for absolute error control of adaptive iterative algorithm (default value 10^10) MaxHalf
(int)Maximum number of substep iterations within an integration step (default value 15)
See also
Modified IbarraMedinaKrawinkler Deterioration Model with Bilinear Hysteretic Response (Bilin Material)Â¶

uniaxialMaterial
('Bilin', matTag, K0, as_Plus, as_Neg, My_Plus, My_Neg, Lamda_S, Lamda_C, Lamda_A, Lamda_K, c_S, c_C, c_A, c_K, theta_p_Plus, theta_p_Neg, theta_pc_Plus, theta_pc_Neg, Res_Pos, Res_Neg, theta_u_Plus, theta_u_Neg, D_Plus, D_Neg, nFactor=0.0) This command is used to construct a bilin material. The bilin material simulates the modified IbarraKrawinkler deterioration model with bilinear hysteretic response. Note that the hysteretic response of this material has been calibrated with respect to more than 350 experimental data of steel beamtocolumn connections and multivariate regression formulas are provided to estimate the deterioration parameters of the model for different connection types. These relationships were developed by Lignos and Krawinkler (2009, 2011) and have been adopted by PEER/ATC (2010). The input parameters for this component model can be computed interactively from this link. Use the module Component Model.
matTag
(int)integer tag identifying material K0
(float)elastic stiffness as_Plus
(float)strain hardening ratio for positive loading direction as_Neg
(float)strain hardening ratio for negative loading direction My_Plus
(float)effective yield strength for positive loading direction My_Neg
(float)effective yield strength for negative loading direction (negative value) Lamda_S
(float)Cyclic deterioration parameter for strength deterioration [E_t=Lamda_S*M_y; set Lamda_S = 0 to disable this mode of deterioration] Lamda_C
(float)Cyclic deterioration parameter for postcapping strength deterioration [E_t=Lamda_C*M_y; set Lamda_C = 0 to disable this mode of deterioration] Lamda_A
(float)Cyclic deterioration parameter for acceleration reloading stiffness deterioration (is not a deterioration mode for a component with Bilinear hysteretic response) [Input value is required, but not used; set Lamda_A = 0]. Lamda_K
(float)Cyclic deterioration parameter for unloading stiffness deterioration [E_t=Lamda_K*M_y; set Lamda_k = 0 to disable this mode of deterioration] c_S
(float)rate of strength deterioration. The default value is 1.0. c_C
(float)rate of postcapping strength deterioration. The default value is 1.0. c_A
(float)rate of accelerated reloading deterioration. The default value is 1.0. c_K
(float)rate of unloading stiffness deterioration. The default value is 1.0. theta_p_Plus
(float)precapping rotation for positive loading direction (often noted as plastic rotation capacity) theta_p_Neg
(float)precapping rotation for negative loading direction (often noted as plastic rotation capacity) (positive value) theta_pc_Plus
(float)postcapping rotation for positive loading direction theta_pc_Neg
(float)postcapping rotation for negative loading direction (positive value) Res_Pos
(float)residual strength ratio for positive loading direction Res_Neg
(float)residual strength ratio for negative loading direction (positive value) theta_u_Plus
(float)ultimate rotation capacity for positive loading direction theta_u_Neg
(float)ultimate rotation capacity for negative loading direction (positive value) D_Plus
(float)rate of cyclic deterioration in the positive loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0. D_Neg
(float)rate of cyclic deterioration in the negative loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0. nFactor
(float)elastic stiffness amplification factor, mainly for use with concentrated plastic hinge elements (optional, default = 0).
See also
Modified IbarraMedinaKrawinkler Deterioration Model with PeakOriented Hysteretic Response (ModIMKPeakOriented Material)Â¶

uniaxialMaterial
('ModIMKPeakOriented', matTag, K0, as_Plus, as_Neg, My_Plus, My_Neg, Lamda_S, Lamda_C, Lamda_A, Lamda_K, c_S, c_C, c_A, c_K, theta_p_Plus, theta_p_Neg, theta_pc_Plus, theta_pc_Neg, Res_Pos, Res_Neg, theta_u_Plus, theta_u_Neg, D_Plus, D_Neg) This command is used to construct a ModIMKPeakOriented material. This material simulates the modified IbarraMedinaKrawinkler deterioration model with peakoriented hysteretic response. Note that the hysteretic response of this material has been calibrated with respect to 200 experimental data of RC beams in order to estimate the deterioration parameters of the model. This information was developed by Lignos and Krawinkler (2012). NOTE: before you use this material make sure that you have downloaded the latest OpenSees version. A youtube video presents a summary of this model including the way to be used within openSees youtube link.
matTag
(int)integer tag identifying material K0
(float)elastic stiffness as_Plus
(float)strain hardening ratio for positive loading direction as_Neg
(float)strain hardening ratio for negative loading direction My_Plus
(float)effective yield strength for positive loading direction My_Neg
(float)effective yield strength for negative loading direction (negative value) Lamda_S
(float)Cyclic deterioration parameter for strength deterioration [E_t=Lamda_S*M_y, see Lignos and Krawinkler (2011); set Lamda_S = 0 to disable this mode of deterioration] Lamda_C
(float)Cyclic deterioration parameter for postcapping strength deterioration [E_t=Lamda_C*M_y, see Lignos and Krawinkler (2011); set Lamda_C = 0 to disable this mode of deterioration] Lamda_A
(float)Cyclic deterioration parameter for accelerated reloading stiffness deterioration [E_t=Lamda_A*M_y, see Lignos and Krawinkler (2011); set Lamda_A = 0 to disable this mode of deterioration] Lamda_K
(float)Cyclic deterioration parameter for unloading stiffness deterioration [E_t=Lamda_K*M_y, see Lignos and Krawinkler (2011); set Lamda_K = 0 to disable this mode of deterioration] c_S
(float)rate of strength deterioration. The default value is 1.0. c_C
(float)rate of postcapping strength deterioration. The default value is 1.0. c_A
(float)rate of accelerated reloading deterioration. The default value is 1.0. c_K
(float)rate of unloading stiffness deterioration. The default value is 1.0. theta_p_Plus
(float)precapping rotation for positive loading direction (often noted as plastic rotation capacity) theta_p_Neg
(float)precapping rotation for negative loading direction (often noted as plastic rotation capacity) (must be defined as a positive value) theta_pc_Plus
(float)postcapping rotation for positive loading direction theta_pc_Neg
(float)postcapping rotation for negative loading direction (must be defined as a positive value) Res_Pos
(float)residual strength ratio for positive loading direction Res_Neg
(float)residual strength ratio for negative loading direction (must be defined as a positive value) theta_u_Plus
(float)ultimate rotation capacity for positive loading direction theta_u_Neg
(float)ultimate rotation capacity for negative loading direction (must be defined as a positive value) D_Plus
(float)rate of cyclic deterioration in the positive loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0. D_Neg
(float)rate of cyclic deterioration in the negative loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0.
See also
Modified IbarraMedinaKrawinkler Deterioration Model with Pinched Hysteretic Response (ModIMKPinching Material)Â¶

uniaxialMaterial
('ModIMKPinching', matTag, K0, as_Plus, as_Neg, My_Plus, My_Neg, FprPos, FprNeg, A_pinch, Lamda_S, Lamda_C, Lamda_A, Lamda_K, c_S, c_C, c_A, c_K, theta_p_Plus, theta_p_Neg, theta_pc_Plus, theta_pc_Neg, Res_Pos, Res_Neg, theta_u_Plus, theta_u_Neg, D_Plus, D_Neg) This command is used to construct a ModIMKPinching material. This material simulates the modified IbarraMedinaKrawinkler deterioration model with pinching hysteretic response. NOTE: before you use this material make sure that you have downloaded the latest OpenSees version. A youtube video presents a summary of this model including the way to be used within openSees youtube link.
matTag
(int)integer tag identifying material K0
(float)elastic stiffness as_Plus
(float)strain hardening ratio for positive loading direction as_Neg
(float)strain hardening ratio for negative loading direction My_Plus
(float)effective yield strength for positive loading direction My_Neg
(float)effective yield strength for negative loading direction (Must be defined as a negative value) FprPos
(float)Ratio of the force at which reloading begins to force corresponding to the maximum historic deformation demand (positive loading direction) FprNeg
(float)Ratio of the force at which reloading begins to force corresponding to the absolute maximum historic deformation demand (negative loading direction) A_pinch
(float)Ratio of reloading stiffness Lamda_S
(float)Cyclic deterioration parameter for strength deterioration [E_t=Lamda_S*M_y, see Lignos and Krawinkler (2011); set Lamda_S = 0 to disable this mode of deterioration] Lamda_C
(float)Cyclic deterioration parameter for postcapping strength deterioration [E_t=Lamda_C*M_y, see Lignos and Krawinkler (2011); set Lamda_C = 0 to disable this mode of deterioration] Lamda_A
(float)Cyclic deterioration parameter for accelerated reloading stiffness deterioration [E_t=Lamda_A*M_y, see Lignos and Krawinkler (2011); set Lamda_A = 0 to disable this mode of deterioration] Lamda_K
(float)Cyclic deterioration parameter for unloading stiffness deterioration [E_t=Lamda_K*M_y, see Lignos and Krawinkler (2011); set Lamda_K = 0 to disable this mode of deterioration] c_S
(float)rate of strength deterioration. The default value is 1.0. c_C
(float)rate of postcapping strength deterioration. The default value is 1.0. c_A
(float)rate of accelerated reloading deterioration. The default value is 1.0. c_K
(float)rate of unloading stiffness deterioration. The default value is 1.0. theta_p_Plus
(float)precapping rotation for positive loading direction (often noted as plastic rotation capacity) theta_p_Neg
(float)precapping rotation for negative loading direction (often noted as plastic rotation capacity) (must be defined as a positive value) theta_pc_Plus
(float)postcapping rotation for positive loading direction theta_pc_Neg
(float)postcapping rotation for negative loading direction (must be defined as a positive value) Res_Pos
(float)residual strength ratio for positive loading direction Res_Neg
(float)residual strength ratio for negative loading direction (must be defined as a positive value) theta_u_Plus
(float)ultimate rotation capacity for positive loading direction theta_u_Neg
(float)ultimate rotation capacity for negative loading direction (must be defined as a positive value) D_Plus
(float)rate of cyclic deterioration in the positive loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0. D_Neg
(float)rate of cyclic deterioration in the negative loading direction (this parameter is used to create assymetric hysteretic behavior for the case of a composite beam). For symmetric hysteretic response use 1.0.
See also
SAWS MaterialÂ¶

uniaxialMaterial
('SAWS', matTag, F0, FI, DU, S0, R1, R2, R3, R4, alpha, beta) This file contains the class definition for SAWSMaterial. SAWSMaterial provides the implementation of a onedimensional hysteretic model develeped as part of the CUREe Caltech wood frame project.
matTag
(int)integer tag identifying material F0
(float)Intercept strength of the shear wall spring element for the asymtotic line to the envelope curve F0 > FI > 0 FI
(float)Intercept strength of the spring element for the pinching branch of the hysteretic curve. (FI > 0). DU
(float)Spring element displacement at ultimate load. (DU > 0). S0
(float)Initial stiffness of the shear wall spring element (S0 > 0). R1
(float)Stiffness ratio of the asymptotic line to the spring element envelope curve. The slope of this line is R1 S0. (0 < R1 < 1.0). R2
(float)Stiffness ratio of the descending branch of the spring element envelope curve. The slope of this line is R2 S0. ( R2 < 0). R3
(float)Stiffness ratio of the unloading branch off the spring element envelope curve. The slope of this line is R3 S0. ( R3 1). R4
(float)Stiffness ratio of the pinching branch for the spring element. The slope of this line is R4 S0. ( R4 > 0). alpha
(float)Stiffness degradation parameter for the shear wall spring element. (ALPHA > 0). beta
(float)Stiffness degradation parameter for the spring element. (BETA > 0).
See also
BarSlip MaterialÂ¶

uniaxialMaterial
('BarSlip', matTag, fc, fy, Es, fu, Eh, db, ld, nb, depth, height, ancLratio=1.0, bsFlag, type, damage='Damage', unit='psi') This command is used to construct a uniaxial material that simulates the bar force versus slip response of a reinforcing bar anchored in a beamcolumn joint. The model exhibits degradation under cyclic loading. Cyclic degradation of strength and stiffness occurs in three ways: unloading stiffness degradation, reloading stiffness degradation, strength degradation.
matTag
(int)integer tag identifying material fc
(float)positive floating point value defining the compressive strength of the concrete in which the reinforcing bar is anchored fy
(float)positive floating point value defining the yield strength of the reinforcing steel Es
(float)floating point value defining the modulus of elasticity of the reinforcing steel fu
(float)positive floating point value defining the ultimate strength of the reinforcing steel Eh
(float)floating point value defining the hardening modulus of the reinforcing steel ld
(float)floating point value defining the development length of the reinforcing steel db
(float)point value defining the diameter of reinforcing steel nb
(int)an integer defining the number of anchored bars depth
(float)floating point value defining the dimension of the member (beam or column) perpendicular to the dimension of the plane of the paper height
(float)floating point value defining the height of the flexural member, perpendicular to direction in which the reinforcing steel is placed, but in the plane of the paper ancLratio
(float)floating point value defining the ratio of anchorage length used for the reinforcing bar to the dimension of the joint in the direction of the reinforcing bar (optional, default: 1.0) bsFlag
(str)string indicating relative bond strength for the anchored reinforcing bar (options: 'Strong'
or'Weak'
)type
(str)string indicating where the reinforcing bar is placed. (options: 'beamtop'
,'beambot'
or'column'
)damage
(str)string indicating type of damage:whether there is full damage in the material or no damage (optional, options: 'Damage'
,'NoDamage'
; default:'Damage'
)unit
(str)string indicating the type of unit system used (optional, options: 'psi'
,'MPa'
,'Pa'
,'psf'
,'ksi'
,'ksf'
) (default:'psi'
/'MPa'
)
See also
Bond SP01   Strain Penetration Model for Fully Anchored Steel Reinforcing BarsÂ¶

uniaxialMaterial
('Bond_SP01', matTag, Fy, Sy, Fu, Su, b, R) This command is used to construct a uniaxial material object for capturing strain penetration effects at the columntofooting, columntobridge bent caps, and walltofooting intersections. In these cases, the bond slip associated with strain penetration typically occurs along a portion of the anchorage length. This model can also be applied to the beam end regions, where the strain penetration may include slippage of the bar along the entire anchorage length, but the model parameters should be chosen appropriately.
This model is for fully anchored steel reinforcement bars that experience bond slip along a portion of the anchorage length due to strain penetration effects, which are usually the case for column and wall longitudinal bars anchored into footings or bridge joints
matTag
(int)integer tag identifying material Fy
(float)Yield strength of the reinforcement steel Sy
(float)Rebar slip at member interface under yield stress. (see NOTES below) Fu
(float)Ultimate strength of the reinforcement steel Su
(float)Rebar slip at the loaded end at the bar fracture strength b
(float)Initial hardening ratio in the monotonic slip vs. bar stress response (0.3~0.5) R
(float)Pinching factor for the cyclic slip vs. bar response (0.5~1.0)
See also
Fatigue MaterialÂ¶

uniaxialMaterial
('Fatigue', matTag, otherTag, 'E0', E0=0.191, 'm', m=0.458, 'min', min=1e16, 'max', max=1e16) The fatigue material uses a modified rainflow cycle counting algorithm to accumulate damage in a material using Minerâs Rule. Element stress/strain relationships become zero when fatigue life is exhausted.
matTag
(int)integer tag identifying material otherTag
(float)Unique material object integer tag for the material that is being wrapped E0
(float)Value of strain at which one cycle will cause failure (default 0.191) m
(float)Slope of CoffinManson curve in loglog space (default 0.458) min
(float)Global minimum value for strain or deformation (default 1e16) max
(float)Global maximum value for strain or deformation (default 1e16)
See also
Impact MaterialÂ¶

uniaxialMaterial
('ImpactMaterial', matTag, K1, K2, sigy, gap) This command is used to construct an impact material object
matTag
(int)integer tag identifying material K1
(float)initial stiffness K2
(float)secondary stiffness sigy
(float)yield displacement gap
(float)initial gap
See also
Hyperbolic Gap MaterialÂ¶

uniaxialMaterial
('HyperbolicGapMaterial', matTag, Kmax, Kur, Rf, Fult, gap) This command is used to construct a hyperbolic gap material object.
matTag
(int)integer tag identifying material Kmax
(float)initial stiffness Kur
(float)unloading/reloading stiffness Rf
(float)failure ratio Fult
(float)ultimate (maximum) passive resistance gap
(float)initial gap
Note
 This material is implemented as a compressiononly gap material.
Fult
andgap
should be input as negative values.  Recomended Values:
Kmax
= 20300 kN/m of abutment widthKcur
=Kmax
Rf
= 0.7Fult
= 326 kN per meter of abutment widthgap
= 2.54 cm
See also
Limit State MaterialÂ¶

uniaxialMaterial
('LimitState', matTag, s1p, e1p, s2p, e2p, s3p, e3p, s1n, e1n, s2n, e2n, s3n, e3n, pinchX, pinchY, damage1, damage2, beta, curveTag, curveType) This command is used to construct a uniaxial hysteretic material object with pinching of force and deformation, damage due to ductility and energy, and degraded unloading stiffness based on ductility. Failure of the material is defined by the associated Limit Curve.
matTag
(int)integer tag identifying material s1p
e1p
(float)stress and strain (or force & deformation) at first point of the envelope in the positive direction s2p
e2p
(float)stress and strain (or force & deformation) at second point of the envelope in the positive direction s3p
e3p
(float)stress and strain (or force & deformation) at third point of the envelope in the positive direction s1n
e1n
(float)stress and strain (or force & deformation) at first point of the envelope in the negative direction s2n
e2n
(float)stress and strain (or force & deformation) at second point of the envelope in the negative direction s3n
e3n
(float)stress and strain (or force & deformation) at third point of the envelope in the negative direction pinchX
(float)pinching factor for strain (or deformation) during reloading pinchY
(float)pinching factor for stress (or force) during reloading damage1
(float)damage due to ductility: D1(m1) damage2
(float)damage due to energy: D2(Ei/Eult) beta
(float)power used to determine the degraded unloading stiffness based on ductility, mb (optional, default=0.0) curveTag
(int)an integer tag for the Limit Curve defining the limit surface curveType
(int)an integer defining the type of LimitCurve (0 = no curve, 1 = axial curve, all other curves can be any other integer)
Note
 negative backbone points should be entered as negative numeric values
See also
MinMax MaterialÂ¶

uniaxialMaterial
('MinMax', matTag, otherTag, 'min', minStrain=1e16, 'max', maxStrain=1e16) This command is used to construct a MinMax material object. This stressstrain behaviour for this material is provided by another material. If however the strain ever falls below or above certain threshold values, the other material is assumed to have failed. From that point on, values of 0.0 are returned for the tangent and stress.
matTag
(int)integer tag identifying material otherTag
(float)tag of the other material minStrain
(float)minimum value of strain. optional default = 1.0e16. maxStrain
(float)max value of strain. optional default = 1.0e16.
See also
ElasticBilin MaterialÂ¶

uniaxialMaterial
('ElasticBilin', matTag, EP1, EP2, epsP2, EN1=EP1, EN2=EP2, epsN2=epsP2) This command is used to construct an elastic bilinear uniaxial material object. Unlike all other bilinear materials, the unloading curve follows the loading curve exactly.
matTag
(int)integer tag identifying material EP1
(float)tangent in tension for stains: 0 <= strains <= epsP2
EP2
(float)tangent when material in tension with strains > epsP2
epsP2
(float)strain at which material changes tangent in tension. EN1
(float)optional, default = EP1
. tangent in compression for stains: 0 < strains <=epsN2
EN2
(float)optional, default = EP2
. tangent in compression with strains <epsN2
epsN2
(float)optional, default = epsP2
. strain at which material changes tangent in compression.
Note
eps0
can not be controlled. It is always zero.
See also
ElasticMultiLinear MaterialÂ¶

uniaxialMaterial
('ElasticMultiLinear', matTag, eta=0.0, 'strain', *strain, 'stress', *stress) This command is used to construct a multilinear elastic uniaxial material object. The nonlinear stressstrain relationship is given by a multilinear curve that is define by a set of points. The behavior is nonlinear but it is elastic. This means that the material loads and unloads along the same curve, and no energy is dissipated. The slope given by the last two specified points on the positive strain axis is extrapolated to infinite positive strain. Similarly, the slope given by the last two specified points on the negative strain axis is extrapolated to infinite negative strain. The number of provided strain points needs to be equal to the number of provided stress points.
matTag
(int)integer tag identifying material eta
(float)damping tangent (optional, default=0.0) strain
(list (float))list of strain points along stressstrain curve stress
(list (float))list of stress points along stressstrain curve
See also
MultiLinearÂ¶

uniaxialMaterial
('MultiLinear', matTag, *pts) This command is used to construct a uniaxial multilinear material object.
matTag
(int)integer tag identifying material pts
(list (float))a list of strain and stress points
pts = [strain1, stress1, strain2, stress2, ..., ]
See also
Initial Strain MaterialÂ¶

uniaxialMaterial
('InitStrainMaterial', matTag, otherTag, initStrain) This command is used to construct an Initial Strain material object. The stressstrain behaviour for this material is defined by another material. Initial Strain Material enables definition of initial strains for the material under consideration. The stress that corresponds to the initial strain will be calculated from the other material.
matTag
(int)integer tag identifying material otherTag
(int)tag of the other material initStrain
(float)initial strain
See also
Initial Stress MaterialÂ¶

uniaxialMaterial
('InitStressMaterial', matTag, otherTag, initStress) This command is used to construct an Initial Stress material object. The stressstrain behaviour for this material is defined by another material. Initial Stress Material enables definition of initial stress for the material under consideration. The strain that corresponds to the initial stress will be calculated from the other material.
matTag
(int)integer tag identifying material otherTag
(float)tag of the other material initStress
(float)initial stress
See also
PathIndependent MaterialÂ¶
Pinching4 MaterialÂ¶

uniaxialMaterial
('Pinching4', matTag, ePf1, ePd1, ePf2, ePd2, ePf3, ePd3, ePf4, ePd4, <eNf1, eNd1, eNf2, eNd2, eNf3, eNd3, eNf4, eNd4>, rDispP, rForceP, uForceP, <rDispN, rForceN, uForceN>, gK1, gK2, gK3, gK4, gKLim, gD1, gD2, gD3, gD4, gDLim, gF1, gF2, gF3, gF4, gFLim, gE, dmgType) This command is used to construct a uniaxial material that represents a âpinchedâ loaddeformation response and exhibits degradation under cyclic loading. Cyclic degradation of strength and stiffness occurs in three ways: unloading stiffness degradation, reloading stiffness degradation, strength degradation.
matTag
(int)integer tag identifying material ePf1
ePf2
ePf3
ePf4
(float)floating point values defining force points on the positive response envelope ePd1
ePd2
ePd3
ePd4
(float)floating point values defining deformation points on the positive response envelope eNf1
eNf2
eNf3
eNf4
(float)floating point values defining force points on the negative response envelope eNd1
eNd2
eNd3
eNd4
(float)floating point values defining deformation points on the negative response envelope rDispP
(float)floating point value defining the ratio of the deformation at which reloading occurs to the maximum historic deformation demand fFoceP
(float)floating point value defining the ratio of the force at which reloading begins to force corresponding to the maximum historic deformation demand uForceP
(float)floating point value defining the ratio of strength developed upon unloading from negative load to the maximum strength developed under monotonic loading rDispN
(float)floating point value defining the ratio of the deformation at which reloading occurs to the minimum historic deformation demand fFoceN
(float)floating point value defining the ratio of the force at which reloading begins to force corresponding to the minimum historic deformation demand uForceN
(float)floating point value defining the ratio of strength developed upon unloading from negative load to the minimum strength developed under monotonic loading gK1
gK2
gK3
gK4
gKLim
(float)floating point values controlling cyclic degradation model for unloading stiffness degradation gD1
gD2
gD3
gD4
gDLim
(float)floating point values controlling cyclic degradation model for reloading stiffness degradation gF1
gF2
gF3
gF4
gFLim
(float)floating point values controlling cyclic degradation model for strength degradation gE
(float)floating point value used to define maximum energy dissipation under cyclic loading. Total energy dissipation capacity is defined as this factor multiplied by the energy dissipated under monotonic loading. dmgType
(str)string to indicate type of damage (option: 'cycle'
,'energy'
)
See also
Engineered Cementitious Composites MaterialÂ¶

uniaxialMaterial
('ECC01', matTag, sigt0, epst0, sigt1, epst1, epst2, sigc0, epsc0, epsc1, alphaT1, alphaT2, alphaC, alphaCU, betaT, betaC) This command is used to construct a uniaxial Engineered Cementitious Composites (ECC)material object based on the ECC material model of Han, et al. (see references). Reloading in tension and compression is linear.
matTag
(int)integer tag identifying material sigt0
(float)tensile cracking stress epst0
(float)strain at tensile cracking stress sigt1
(float)peak tensile stress epst1
(float)strain at peak tensile stress epst2
(float)ultimate tensile strain sigc0
(float)compressive strength (see NOTES) epsc0
(float)strain at compressive strength (see NOTES) epsc1
(float)ultimate compressive strain (see NOTES) alphaT1
(float)exponent of the unloading curve in tensile strain hardening region alphaT2
(float)exponent of the unloading curve in tensile softening region alphaC
(float)exponent of the unloading curve in the compressive softening alphaCU
(float)exponent of the compressive softening curve (use 1 for linear softening) betaT
(float)parameter to determine permanent strain in tension betaC
(float)parameter to determine permanent strain in compression
See also
SelfCentering MaterialÂ¶

uniaxialMaterial
('SelfCentering', matTag, k1, k2, sigAct, beta, epsSlip=0, epsBear=0, rBear=k1) This command is used to construct a uniaxial selfcentering (flagshaped) material object with optional nonrecoverable slip behaviour and an optional stiffness increase at high strains (bearing behaviour).
matTag
(int)integer tag identifying material k1
(float)Initial Stiffness k2
(float)PostActivation Stiffness (0< k2``< ``k1
)sigAct
(float)Forward Activation Stress/Force beta
(float)Ratio of Forward to Reverse Activation Stress/Force epsSlip
(float)slip Strain/Deformation (if epsSlip
= 0, there will be no slippage)epsBear
(float)Bearing Strain/Deformation (if epsBear
= 0, there will be no bearing)rBear
(float)Ratio of Bearing Stiffness to Initial Stiffness k1
See also
Viscous MaterialÂ¶

uniaxialMaterial
('Viscous', matTag, C, alpha) This command is used to construct a uniaxial viscous material object. stress =C(strainrate)^alpha
matTag
(int)integer tag identifying material C
(float)damping coeficient alpha
(float)power factor (=1 means linear damping)
Note
 This material can only be assigned to truss and zeroLength elements.
 This material can not be combined in parallel/series with other materials. When defined in parallel with other materials it is ignored.
See also
BoucWen MaterialÂ¶

uniaxialMaterial
('BoucWen', matTag, alpha, ko, n, gamma, beta, Ao, deltaA, deltaNu, deltaEta) This command is used to construct a uniaxial BoucWen smooth hysteretic material object. This material model is an extension of the original BoucWen model that includes stiffness and strength degradation (Baber and Noori (1985)).
matTag
(int)integer tag identifying material alpha
(float)ratio of postyield stiffness to the initial elastic stiffenss (0< alpha <1) ko
(float)initial elastic stiffness n
(float)parameter that controls transition from linear to nonlinear range (as n increases the transition becomes sharper; n is usually grater or equal to 1) gamma
beta
(float)parameters that control shape of hysteresis loop; depending on the values of gamma and beta softening, hardening or quasilinearity can be simulated (look at the NOTES) Ao
deltaA
(float)parameters that control tangent stiffness deltaNu
deltaEta
(float)parameters that control material degradation
See also
BWBN MaterialÂ¶

uniaxialMaterial
('BWBN', matTag, alpha, ko, n, gamma, beta, Ao, q, zetas, p, Shi, deltaShi, lambda, tol, maxIter) This command is used to construct a uniaxial BoucWen pinching hysteretic material object. This material model is an extension of the original BoucWen model that includes pinching (Baber and Noori (1986) and Foliente (1995)).
matTag
(int)integer tag identifying material alpha
(float)ratio of postyield stiffness to the initial elastic stiffenss (0< alpha <1) ko
(float)initial elastic stiffness n
(float)parameter that controls transition from linear to nonlinear range (as n increases the transition becomes sharper; n is usually grater or equal to 1) gamma
beta
(float)parameters that control shape of hysteresis loop; depending on the values of gamma and beta softening, hardening or quasilinearity can be simulated (look at the BoucWen Material) Ao
(float)parameter that controls tangent stiffness q
zetas
p
Shi
deltaShi
lambda
(float)parameters that control pinching tol
(float)tolerance maxIter
(float)maximum iterations
See also
KikuchiAikenHDR MaterialÂ¶

uniaxialMaterial
('KikuchiAikenHDR', matTag, tp, ar, hr, <'coGHU', cg, ch, cu>, <'coMSS', rs, rf>) This command is used to construct a uniaxial KikuchiAikenHDR material object. This material model produces nonlinear hysteretic curves of high damping rubber bearings (HDRs).
matTag
(int)integer tag identifying material tp
(str)rubber type (see note 1) ar
(float)area of rubber [unit: m^2] (see note 2) hr
(float)total thickness of rubber [unit: m] (see note 2) cg
ch
cu
(float)correction coefficients for equivalent shear modulus ( cg
), equivalent viscous daming ratio (ch
), ratio of shear force at zero displacement (cu
).rs
rf
(float)reduction rate for stiffness ( rs
) and force (rf
) (see note 3)
Note
 Following rubber types for
tp
are available:'X0.6'
Bridgestone X0.6, standard compressive stress, up to 400% shear strain'X0.60MPa'
Bridgestone X0.6, zero compressive stress, up to 400% shear strain'X0.4'
Bridgestone X0.4, standard compressive stress, up to 400% shear strain'X0.40MPa'
Bridgestone X0.4, zero compressive stress, up to 400% shear strain'X0.3'
Bridgestone X0.3, standard compressive stress, up to 400% shear strain'X0.30MPa'
Bridgestone X0.3, zero compressive stress, up to 400% shear strain
 This material uses SI unit in calculation formula.
ar
andhr
must be converted into [m^2] and [m], respectively. rs
andrf
areăavailable if this material is applied to multipleShearSpring (MSS) element. Recommended values arers
= \(\frac{1}{\sum_{i=0}^{n1}\sin(\pi*i/n)^2}\) andrf
= \(\frac{1}{\sum_{i=0}^{n1}\sin(\pi*i/n)}\), where n is the number of springs in the MSS. For example, when n=8,rs
=0.2500,rf
=0.1989.
See also
KikuchiAikenLRB MaterialÂ¶

uniaxialMaterial
('KikuchiAikenLRB', matTag, type, ar, hr, gr, ap, tp, alph, beta, <'T', temp>, <'coKQ', rk, rq>, <'coMSS', rs, rf>) This command is used to construct a uniaxial KikuchiAikenLRB material object. This material model produces nonlinear hysteretic curves of leadrubber bearings.
matTag
(int)integer tag identifying material type
(int)rubber type (see note 1) ar
(float)area of rubber [unit: m^2] hr
(float)total thickness of rubber [unit: m] gr
(float)shear modulus of rubber [unit: N/m^2] ap
(float)area of lead plug [unit: m^2] tp
(float)yield stress of lead plug [unit: N/m^2] alph
(float)shear modulus of lead plug [unit: N/m^2] beta
(float)ratio of initial stiffness to yielding stiffness temp
(float)temperature [unit: Â°C] rk
rq
(float)reduction rate for yielding stiffness ( rk
) and force at zero displacement (rq
)rs
rf
(float)reduction rate for stiffness ( rs
) and force (rf
) (see note 3)
Note
 Following rubber types for
type
are available:1
leadrubber bearing, up to 400% shear strain [Kikuchi et al., 2010 & 2012]
 This material uses SI unit in calculation formula. Input arguments must be converted into [m], [m^2], [N/m^2].
rs
andrf
are available if this material is applied to multipleShearSpring (MSS) element. Recommended values arers
= \(\frac{1}{\sum_{i=0}^{n1}\sin(\pi*i/n)^2}\) andrf
= \(\frac{1}{\sum_{i=0}{n1}\sin(\pi*i/n)}\), where n is the number of springs in the MSS. For example, when n=8,rs
= 0.2500 andrf
= 0.1989.
See also
AxialSp MaterialÂ¶

uniaxialMaterial
('AxialSp', matTag, sce, fty, fcy, <bte, bty, bcy, fcr>) This command is used to construct a uniaxial AxialSp material object. This material model produces axial stressstrain curve of elastomeric bearings.
matTag
(int)integer tag identifying material sce
(float)compressive modulus fty
fcy
(float)yield stress under tension ( fty
) and compression (fcy
) (see note 1)bte
bty
bcy
(float)reduction rate for tensile elastic range ( bte
), tensile yielding (bty
) and compressive yielding (bcy
) (see note 1)fcr
(float)target point stress (see note 1)
Note
Input parameters are required to satisfy followings.
fcy
< 0.0 <fty
0.0 <=
bty
<bte
<= 1.00.0 <=
bcy
<= 1.0fcy
<=fcr
<= 0.0
See also
AxialSpHD MaterialÂ¶

uniaxialMaterial
('AxialSpHD', matTag, sce, fty, fcy, <bte, bty, bth, bcy, fcr, ath>) This command is used to construct a uniaxial AxialSpHD material object. This material model produces axial stressstrain curve of elastomeric bearings including hardening behavior.
matTag
(int)integer tag identifying material sce
(float)compressive modulus fty
fcy
(float)yield stress under tension ( fty
) and compression (fcy
) (see note 1)bte
bty
bth
bcy
(float)reduction rate for tensile elastic range ( bte
), tensile yielding (bty
), tensile hardening (bth
) and compressive yielding (bcy
) (see note 1)fcr
(float)target point stress (see note 1) ath
(float)hardening strain ratio to yield strain
Note
Input parameters are required to satisfy followings.
fcy
< 0.0 <fty
0.0 <=
bty
<bth
<bte
<= 1.00.0 <=
bcy
<= 1.0fcy
<=fcr
<= 0.01.0 <=
ath
See also
Pinching Limit State MaterialÂ¶
This command is used to construct a uniaxial material that simulates a pinched loaddeformation response and exhibits degradation under cyclic loading. This material works with the RotationShearCurve limit surface that can monitor a key deformation and/or a key force in an associated frame element and trigger a degrading behavior in this material when a limiting value of the deformation and/or force are reached. The material can be used in two modes: 1) direct input mode, where pinching and damage parameters are directly input; and 2) calibrated mode for shearcritical concrete columns, where only key column properties are input for model to fully define pinching and damage parameters.

uniaxialMaterial
('PinchingLimitStateMaterial', matTag, nodeT, nodeB, driftAxis, Kelas, crvTyp, crvTag, YpinchUPN, YpinchRPN, XpinchRPN, YpinchUNP, YpinchRNP, XpinchRNP, dmgStrsLimE, dmgDispMax, dmgE1, dmgE2, dmgE3, dmgE4, dmgELim, dmgR1, dmgR2, dmgR3, dmgR4, dmgRLim, dmgRCyc, dmgS1, dmgS2, dmgS3, dmgS4, dmgSLim, dmgSCyc) MODE 1: Direct Input
matTag
(int)integer tag identifying material nodeT
(int)integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure) nodeB
(int)integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure) driftAxis
(int)integer to indicate the drift axis in which lateralstrength degradation will occur. This axis should be orthogonal to the axis of measured rotation (see
rotAxis
in Rotation Shear Curve definition)driftAxis
= 1  Drift along the xaxisdriftAxis
= 2  Drift along the yaxisdriftAxis
= 3  Drift along the zaxisKelas
(float)floating point value to define the initial material elastic stiffness (Kelastic); Kelas > 0 crvTyp
(int)integer flag to indicate the type of limit curve associated with this material.
crvTyp
= 0  No limit curvecrvTyp
= 1  axial limit curvecrvTyp
= 2  RotationShearCurvecrvTag
(int)integer tag for the unique limit curve object associated with this material YpinchUPN
(float)floating point unloading force pinching factor for loading in the negative direction. Note: This value must be between zero and unity YpinchRPN
(float)floating point reloading force pinching factor for loading in the negative direction. Note: This value must be between negative one and unity XpinchRPN
(float)floating point reloading displacement pinching factor for loading in the negative direction. Note: This value must be between negative one and unity YpinchUNP
(float)floating point unloading force pinching factor for loading in the positive direction. Note: This value must be between zero and unity YpinchRNP
(float)floating point reloading force pinching factor for loading in the positive direction. Note: This value must be between negative one and unity XpinchRNP
(float)floating point reloading displacement pinching factor for loading in the positive direction. Note: This value must be between negative one and unity dmgStrsLimE
(float)floating point force limit for elastic stiffness damage (typically defined as the lowest of shear strength or shear at flexrual yielding). This value is used to compute the maximum deformation at flexural yield (ÎŽmax Eq. 1) and using the initial elastic stiffness (Kelastic) the monotonic energy (Emono Eq. 1) to yield. Input 1 if this type of damage is not required and set dmgE1
,dmgE2
,dmgE3
,dmgE4
, anddmgELim
to zerodmgDispMax
(float)floating point for ultimate drift at failure (ÎŽmax Eq. 1) and is used for strength and stiffness damage. This value is used to compute the monotonic energy at axial failure (Emono Eq. 2) by computing the area under the backbone in the positive loading direction up to ÎŽmax. Input 1 if this type of damage is not required and set dmgR1
,dmgR2
,dmgR3
,dmgR4
, anddmgRLim
to zero for reloading stiffness damage. Similarly setdmgS1
,dmgS2
,dmgS3
,dmgS4
, anddmgSLim
to zero if reloading strength damage is not requireddmgE1
dmgE2
(float)floating point elastic stiffness damage factors Î±1,Î±2,Î±3,Î±4 shown in Eq. 1 dmgE3
dmgE4
(float)floating point elastic stiffness damage factors Î±1,Î±2,Î±3,Î±4 shown in Eq. 1 dmgELim
(float)floating point elastic stiffness damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity dmgR1
dmgR2
(float)floating point reloading stiffness damage factors Î±1,Î±2,Î±3,Î±4 shown in Eq. 1 dmgR3
dmgR4
(float)floating point reloading stiffness damage factors Î±1,Î±2,Î±3,Î±4 shown in Eq. 1 dmgRLim
(float)floating point reloading stiffness damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity dmgRCyc
(float)floating point cyclic reloading stiffness damage index; Note: This value must be between zero and unity dmgS1
dmgS2
(float)floating point backbone strength damage factors Î±1,Î±2,Î±3,Î±4 shown in Eq. 1 dmgS3
dmgS4
(float)floating point backbone strength damage factors Î±1,Î±2,Î±3,Î±4 shown in Eq. 1 dmgSLim
(float)floating point backbone strength damage limit Dlim shown in Eq. 1; Note: This value must be between zero and unity dmgSCyc
(float)floating point cyclic backbone strength damage index; Note: This value must be between zero and unity

uniaxialMaterial
('PinchingLimitStateMaterial', matTag, dnodeT, nodeB, driftAxis, Kelas, crvTyp, crvTag, eleTag, b, d, h, a, st, As, Acc, ld, db, rhot, fc, fy, fyt) MODE 2: Calibrated Model for ShearCritical Concrete Columns
matTag
(int)integer tag identifying material nodeT
(int)integer node tag to define the first node at the extreme end of the associated flexural frame member (L3 or D5 in Figure) nodeB
(int)integer node tag to define the last node at the extreme end of the associated flexural frame member (L2 or D2 in Figure) driftAxis
(int)integer to indicate the drift axis in which lateralstrength degradation will occur. This axis should be orthogonal to the axis of measured rotation (see
rotAxis`
in Rotation Shear Curve definition)driftAxis
= 1  Drift along the xaxisdriftAxis
= 2  Drift along the yaxisdriftAxis
= 3  Drift along the zaxisKelas
(float)floating point value to define the shear stiffness (Kelastic) of the shear spring prior to shear failure
Kelas
= 4  Shear stiffness calculated assuming double curvature and shear springs at both column element endsKelas
= 3  Shear stiffness calculated assuming double curvature and a shear spring at one column element endKelas
= 2  Shear stiffness calculated assuming single curvature and shear springs at both column element endsKelas
= 1  Shear stiffness calculated assuming single curvature and a shear spring at one column element endKelas
> 0  Shear stiffness is the input valueNote: integer inputs allow the model to know whether column height equals the shear span (cantelever) or twice the shear span (double curvature). For columns in frames, input the value for the case that best approximates column end conditions or manually input shear stiffness (typically double curvature better estimates framed column behavior)
crvTag
(int)integer tag for the unique limit curve object associated with this material eleTag
(int)integer element tag to define the associated beamcolumn element used to extract axial load b
(float)floating point column width (inches) d
(float)floating point column depth (inches) h
(float)floating point column height (inches) a
(float)floating point shear span length (inches) st
(float)floating point transverse reinforcement spacing (inches) along column height As
(float)floating point total area (inches squared) of longitudinal steel bars in section Acc
(float)floating point gross confined concrete area (inches squared) bounded by the transverse reinforcement in column section ld
(float)floating point development length (inches) of longitudinal bars using ACI 31811 Eq. 121 and Eq. 122 db
(float)floating point diameter (inches) of longitudinal bars in column section rhot
(float)floating point transverse reinforcement ratio (Ast/st.db) f'c
(float)floating point concrete compressive strength (ksi) fy
(float)floating point longitudinal steel yield strength (ksi) fyt
(float)floating point transverse steel yield strength (ksi)
See also
CFSWSWP WoodSheathed ColdFormed Steel Shear Wall PanelÂ¶

uniaxialMaterial
('CFSWSWP', matTag, height, width, fut, tf, Ife, Ifi, ts, np, ds, Vs, sc, nc, type, openingArea, openingLength) This command is used to construct a uniaxialMaterial model that simulates the hysteresis response (Shear strengthLateral displacement) of a woodsheathed coldformed steel shear wall panel (CFSSWP). The hysteresis model has smooth curves and takes into account the strength and stiffness degradation, as well as pinching effect.
This uniaxialMaterial gives results in Newton and Meter units, for strength and displacement, respectively.
matTag
(int)integer tag identifying material height
(float)SWPâs height (mm) width
(float)SWPâs width (mm) fut
(float)Tensile strength of framing members (MPa) tf
(float)Framing thickness (mm) Ife
(float)Moment of inertia of the double endstud (mm4) Ifi
(float)Moment of inertia of the intermediate stud (mm4) ts
(float)Sheathing thickness (mm) np
(float)Sheathing number (one or two sides sheathed) ds
(float)Screws diameter (mm) Vs
(float)Screws shear strength (N) sc
(float)Screw spacing on the SWP perimeter (mm) nc
(float)Total number of screws located on the SWP perimeter type
(int)Integer identifier used to define wood sheathing type (DFP=1, OSB=2, CSP=3) openingArea
(float)Total area of openings (mm2) openingLength
(float)Cumulative length of openings (mm)
See also
CFSSSWP SteelSheathed Coldformed Steel Shear Wall PanelÂ¶

uniaxialMaterial
('CFSSSWP', matTag, height, width, fuf, fyf, tf, Af, fus, fys, ts, np, ds, Vs, sc, dt, openingArea, openingLength) This command is used to construct a uniaxialMaterial model that simulates the hysteresis response (Shear strengthlateral Displacement) of a SteelSheathed ColdFormed Steel Shear Wall Panel (CFSSWP). The hysteresis model has smooth curves and takes into account the strength and stiffness degradation, as well as pinching effect.
This uniaxialMaterial gives results in Newton and Meter units, for strength and displacement, respectively.
matTag
(int)integer tag identifying material height
(float)SWPâs height (mm) width
(float)SWPâs width (mm) fuf
(float)Tensile strength of framing members (MPa) fyf
(float)Yield strength of framing members (MPa) tf
(float)Framing thickness (mm) Af
(float)Framing cross section area (mm2) fus
(float)Tensile strength of steel sheet sheathing (MPa) fys
(float)Yield strength of steel sheet sheathing (MPa) ts
(float)Sheathing thickness (mm) np
(float)Sheathing number (one or two sides sheathed) ds
(float)Screws diameter (mm) Vs
(float)Screws shear strength (N) sc
(float)Screw spacing on the SWP perimeter (mm) dt
(float)Anchor boltâs diameter (mm) openingArea
(float)Total area of openings (mm2) openingLength
(float)Cumulative length of openings (mm)
See also
nDMaterial commandsÂ¶

nDMaterial
(matType, matTag, *matArgs)Â¶ This command is used to construct an NDMaterial object which represents the stressstrain relationship at the gausspoint of a continuum element.
matType
(str)material type matTag
(int)material tag. matArgs
(list)a list of material arguments, must be preceded with *
.
For example,
matType = 'ElasticIsotropic'
matTag = 1
matArgs = [E, v]
nDMaterial(matType, matTag, *matArgs)
Standard ModelsÂ¶
The following contain information about available matType
:
 ElasticIsotropic
 ElasticOrthotropic
 J2Plasticity
 DruckerPrager
 Damage2p
 PlaneStress
 PlaneStrain
 MultiaxialCyclicPlasticity
 BoundingCamClay
 PlateFiber
 FSAM
 ManzariDafalias
 PM4Sand
 StressDensityModel
 AcousticMedium
ElasticIsotropicÂ¶

nDMaterial
('ElasticIsotropic', matTag, E, nu, rho=0.0) This command is used to construct an ElasticIsotropic material object.
matTag
(int)integer tag identifying material E
(float)elastic modulus nu
(float)Poissonâs ratio rho
(float)mass density (optional)
The material formulations for the ElasticIsotropic object are:
'ThreeDimensional'
'PlaneStrain'
'Plane Stress'
'AxiSymmetric'
'PlateFiber'
ElasticOrthotropicÂ¶

nDMaterial
('ElasticOrthotropic', matTag, Ex, Ey, Ez, nu_xy, nu_yz, nu_zx, Gxy, Gyz, Gzx, rho=0.0) This command is used to construct an ElasticOrthotropic material object.
matTag
(int)integer tag identifying material Ex
(float)elastic modulus in x direction Ey
(float)elastic modulus in y direction Ez
(float)elastic modulus in z direction nu_xy
(float)Poissonâs ratios in x and y plane nu_yz
(float)Poissonâs ratios in y and z plane nu_zx
(float)Poissonâs ratios in z and x plane Gxy
(float)shear modulii in x and y plane Gyz
(float)shear modulii in y and z plane Gzx
(float)shear modulii in z and x plane rho
(float)mass density (optional)
The material formulations for the ElasticOrthotropic object are:
'ThreeDimensional'
'PlaneStrain'
'Plane Stress'
'AxiSymmetric'
'BeamFiber'
'PlateFiber'
J2PlasticityÂ¶

nDMaterial
('J2Plasticity', matTag, K, G, sig0, sigInf, delta, H) This command is used to construct an multi dimensional material object that has a von Mises (J2) yield criterium and isotropic hardening.
matTag
(int)integer tag identifying material K
(float)bulk modulus G
(float)shear modulus sig0
(float)initial yield stress sigInf
(float)final saturation yield stress delta
(float)exponential hardening parameter H
(float)linear hardening parameter
The material formulations for the J2Plasticity object are:
'ThreeDimensional'
'PlaneStrain'
'Plane Stress'
'AxiSymmetric'
'PlateFiber'
J2 isotropic hardening material class
Elastic Model
Yield Function
Saturation Isotropic Hardening with linear term
Flow Rules
Linear Viscosity
Backward Euler Integration Routine Yield condition enforced at time n+1
set \(\eta\) = 0 for rate independent case
DruckerPragerÂ¶

nDMaterial
('DruckerPrager', matTag, K, G, sigmaY, rho, rhoBar, Kinf, Ko, delta1, delta2, H, theta, density, atmPressure=101e3) This command is used to construct an multi dimensional material object that has a DruckerPrager yield criterium.
matTag
(int)integer tag identifying material K
(float)bulk modulus G
(float)shear modulus sigmaY
(float)yield stress rho
(float)frictional strength parameter rhoBar
(float)controls evolution of plastic volume change, \(0\le rhoBar \le rho\). Kinf
(float)nonlinear isotropic strain hardening parameter, \(Kinf \ge 0\). Ko
(float)nonlinear isotropic strain hardening parameter, \(Ko \ge 0\). delta1
(float)nonlinear isotropic strain hardening parameter, \(delta1\ge 0\). delta2
(float)tension softening parameter, \(delta2\ge 0\). H
(float)linear hardening parameter, \(H \ge 0\). theta
(float)controls relative proportions of isotropic and kinematic hardening, \(0 \le theta \le 1\). density
(float)mass density of the material atmPressure
(float)optional atmospheric pressure for update of elastic bulk and shear moduli
The material formulations for the DrukerPrager object are:
'ThreeDimensional'
'PlaneStrain'
See theory.
Damage2pÂ¶

nDMaterial
('Damage2p', matTag, fcc, 'fct', fct, 'E', E, 'ni', ni, 'Gt', Gt, 'Gc', Gc, 'rho_bar', rho_bar, 'H', H, 'theta', theta, 'tangent', tangent) This command is used to construct a threedimensional material object that has a DruckerPrager plasticity model coupled with a twoparameter damage model.
matTag
(int)integer tag identifying material fcc
(float)concrete compressive strength, negative real value (positive input is changed in sign automatically) fct
(float)optional concrete tensile strength, positive real value (for concrete like materials is less than fcc), \(0.1*abs(fcc)\) = \(4750*sqrt(abs(fcc))\text{ }if\text{ }abs(fcc)<2000\) because fcc is assumed in MPa (see ACI 318) E
(float)optional Young modulus, \(57000*sqrt(abs(fcc))\) if \(abs(fcc)>2000\) because fcc is assumed in psi (see ACI 318) ni
(float)optional Poisson coefficient, 0.15 (from comparison with tests by Kupfer Hilsdorf Rusch 1969) Gt
(float)optional tension fracture energy density, positive real value (integral of the stressstrain envelope in tension), \(1840*fct*fct/E\) (from comparison with tests by Gopalaratnam and Shah 1985) Gc
(float)optional compression fracture energy density, positive real value (integral of the stressstrain envelope after the peak in compression), :math:6250*fcc*fcc/E` (from comparison with tests by Karsan and Jirsa 1969) rho_bar
(float)optional parameter of plastic volume change, positive real value \(0=rhoBar< sqrt(2/3)\), 0.2 (from comparison with tests by Kupfer Hilsdorf Rusch 1969) H
(float)optional linear hardening parameter for plasticity, positive real value (usually less than E), \(0.25*E\) (from comparison with tests by Karsan and Jirsa 1969 and Gopalaratnam and Shah 1985) theta
(float)optional ratio between isotropic and kinematic hardening, positive real value \(0=theta=1\) (with: 0 hardening kinematic only and 1 hardening isotropic only, 0.5 (from comparison with tests by Karsan and Jirsa 1969 and Gopalaratnam and Shah 1985) tangent
(float)optional integer to choose the computational stiffness matrix, 0: computational tangent; 1: damaged secant stiffness (hint: in case of strong nonlinearities use it with KrylovNewton algorithm)
The material formulations for the Damage2p object are:
'ThreeDimensional'
'PlaneStrain'
'Plane Stress'
'AxiSymmetric'
'PlateFiber'
See also here
PlaneStressÂ¶

nDMaterial
('PlaneStress', matTag, mat3DTag) This command is used to construct a planestress material wrapper which converts any threedimensional material into a plane stress material via static condensation.
matTag
(int)integer tag identifying material mat3DTag
(int)tag of perviously defined 3d ndMaterial material
The material formulations for the PlaneStress object are:
'Plane Stress'
PlaneStrainÂ¶

nDMaterial
('PlaneStrain', matTag, mat3DTag) This command is used to construct a planestress material wrapper which converts any threedimensional material into a plane strain material by imposing plain strain conditions on the threedimensional material.
matTag
(int)integer tag identifying material mat3DTag
(int)integer tag of previously defined 3d ndMaterial material
The material formulations for the PlaneStrain object are:
'PlaneStrain'
MultiaxialCyclicPlasticityÂ¶

nDMaterial
('MultiaxialCyclicPlasticity', matTag, rho, K, G, Su, Ho, h, m, beta, KCoeff) This command is used to construct an multiaxial Cyclic Plasticity model for clays
matTag
(int)integer tag identifying material rho
(float)density K
(float)buck modulus G
(float)maximum (small strain) shear modulus Su
(float)undrained shear strength, size of bounding surface \(R=\sqrt{8/3}*Su\) Ho
(float)linear kinematic hardening modulus of bounding surface h
(float)hardening parameter m
(float)hardening parameter beta
(float)integration parameter, usually beta=0.5 KCoeff
(float)coefficient of earth pressure, K0
BoundingCamClayÂ¶

nDMaterial
('BoundingCamClay', matTag, massDensity, C, bulkMod, OCR, mu_o, alpha, lambda, h, m) This command is used to construct a multidimensional bounding surface Cam Clay material object after Borja et al. (2001).
matTag
(int)integer tag identifying material massDensity
(float)mass density C
(float)ellipsoidal axis ratio (defines shape of ellipsoidal loading/bounding surfaces) bulkMod
(float)initial bulk modulus OCR
(float)overconsolidation ratio mu_o
(float)initial shear modulus alpha
(float)pressuredependency parameter for modulii (greater than or equal to zero) lambda
(float)soil compressibility index for virgin loading h
(float)hardening parameter for plastic response inside of bounding surface (if h = 0, no hardening) m
(float)hardening parameter (exponent) for plastic response inside of bounding surface (if m = 0, only linear hardening)
The material formulations for the BoundingCamClay object are:
'ThreeDimensional'
'PlaneStrain'
See also for information
PlateFiberÂ¶

nDMaterial
('PlateFiber', matTag, threeDTag) This command is used to construct a platefiber material wrapper which converts any threedimensional material into a plate fiber material (by static condensation) appropriate for shell analysis.
matTag
(int)integer tag identifying material threeDTag
(float)material tag for a previouslydefined threedimensional material
FSAMÂ¶

nDMaterial
('FSAM', matTag, rho, sXTag, sYTag, concTag, rouX, rouY, nu, alfadow) This command is used to construct a nDMaterial FSAM (FixedStrutAngleModel, Figure 1, Kolozvari et al., 2015), which is a planestress constitutive model for simulating the behavior of RC panel elements under generalized, inplane, reversedcyclic loading conditions (Ulugtekin, 2010; Orakcal et al., 2012). In the FSAM constitutive model, the strain fields acting on concrete and reinforcing steel components of a RC panel are assumed to be equal to each other, implying perfect bond assumption between concrete and reinforcing steel bars. While the reinforcing steel bars develop uniaxial stresses under strains in their longitudinal direction, the behavior of concrete is defined using stressstrain relationships in biaxial directions, the orientation of which is governed by the state of cracking in concrete. Although the concrete stressstrain relationship used in the FSAM is fundamentally uniaxial in nature, it also incorporates biaxial softening effects including compression softening and biaxial damage. For transfer of shear stresses across the cracks, a frictionbased elastoplastic shear aggregate interlock model is adopted, together with a linear elastic model for representing dowel action on the reinforcing steel bars (Kolozvari, 2013). Note that FSAM constitutive model is implemented to be used with ShearFlexure Interaction model for RC walls (SFI_MVLEM), but it could be also used elsewhere.
matTag
(int)integer tag identifying material rho
(float)Material density sXTag
(int)Tag of uniaxialMaterial simulating horizontal (x) reinforcement sYTag
(int)Tag of uniaxialMaterial simulating vertical (y) reinforcement concTag
(int)Tag of uniaxialMaterial simulating concrete, shall be used with uniaxialMaterial ConcreteCM rouX
(float)Reinforcing ratio in horizontal (x) direction (\(rouX = _{s,x}/A_{gross,x}\)) rouY
(float)Reinforcing ratio in vertical (x) direction (\(rouY = _{s,y}/A_{gross,y}\)) nu
(float)Concrete friction coefficient (\(0.0 < \nu < 1.5\)) alfadow
(float)Stiffness coefficient of reinforcement dowel action (\(0.0 < alfadow < 0.05\))
See also here
References:
 Kolozvari K., Orakcal K., and Wallace J. W. (2015). âShearFlexure Interaction Modeling of reinforced Concrete Structural Walls and Columns under Reversed Cyclic Loadingâ, Pacific Earthquake Engineering Research Center, University of California, Berkeley, PEER Report No. 2015/12
 Kolozvari K. (2013). âAnalytical Modeling of Cyclic ShearFlexure Interaction in Reinforced Concrete Structural Wallsâ, PhD Dissertation, University of California, Los Angeles.
 Orakcal K., Massone L.M., and Ulugtekin D. (2012). âConstitutive Modeling of Reinforced Concrete Panel Behavior under Cyclic Loadingâ, Proceedings, 15th World Conference on Earthquake Engineering, Lisbon, Portugal.
 Ulugtekin D. (2010). âAnalytical Modeling of Reinforced Concrete Panel Elements under Reversed Cyclic Loadingsâ, M.S. Thesis, Bogazici University, Istanbul, Turkey.
ManzariDafaliasÂ¶

nDMaterial
('ManzariDafalias', matTag, G0, nu, e_init, Mc, c, lambda_c, e0, ksi, P_atm, m, h0, ch, nb, A0, nd, z_max, cz, Den) This command is used to construct a multidimensional ManzariDafalias(2004) material.
matTag
(int)integer tag identifying material G0
(float)shear modulus constant nu
(float)poisson ratio e_init
(float)initial void ratio Mc
(float)critical state stress ratio c
(float)ratio of critical state stress ratio in extension and compression lambda_c
(float)critical state line constant e0
(float)critical void ratio at p = 0 ksi
(float)critical state line constant P_atm
(float)atmospheric pressure m
(float)yield surface constant (radius of yield surface in stress ratio space) h0
(float)constant parameter ch
(float)constant parameter nb
(float)bounding surface parameter, \(nb \ge 0\) A0
(float)dilatancy parameter nd
(float)dilatancy surface parameter \(nd \ge 0\) z_max
(float)fabricdilatancy tensor parameter cz
(float)fabricdilatancy tensor parameter Den
(float)mass density of the material
The material formulations for the ManzariDafalias object are:
'ThreeDimensional'
'PlaneStrain'
See also here
References
Dafalias YF, Manzari MT. âSimple plasticity sand model accounting for fabric change effectsâ. Journal of Engineering Mechanics 2004
PM4SandÂ¶

nDMaterial
('PM4Sand', matTag, D_r, G_o, h_po, Den, P_atm, h_o, e_max, e_min, n_b, n_d, A_do, z_max, c_z, c_e, phi_cv, nu, g_degr, c_dr, c_kaf, Q_bolt, R_bolt, m_par, F_sed, p_sed) This command is used to construct a 2dimensional PM4Sand material.
matTag
(int)integer tag identifying material D_r
(float)Relative density, in fraction G_o
(float)Shear modulus constant h_po
(float)Contraction rate parameter Den
(float)Mass density of the material P_atm
(float)Optional, Atmospheric pressure h_o
(float)Optional, Variable that adjusts the ratio of plastic modulus to elastic modulus e_max
(float)Optional, Maximum and minimum void ratios e_min
(float)Optional, Maximum and minimum void ratios n_b
(float)Optional, Bounding surface parameter, \(n_b \ge 0\) n_d
(float)Optional, Dilatancy surface parameter \(n_d \ge 0\) A_do
(float)Optional, Dilatancy parameter, will be computed at the time of initialization if input value is negative z_max
(float)Optional, Fabricdilatancy tensor parameter c_z
(float)Optional, Fabricdilatancy tensor parameter c_e
(float)Optional, Variable that adjusts the rate of strain accumulation in cyclic loading phi_cv
(float)Optional, Critical state effective friction angle nu
(float)Optional, Poissonâs ratio g_degr
(float)Optional, Variable that adjusts degradation of elastic modulus with accumulation of fabric c_dr
(float)Optional, Variable that controls the rotated dilatancy surface c_kaf
(float)Optional, Variable that controls the effect that sustained static shear stresses have on plastic modulus Q_bolt
(float)Optional, Critical state line parameter R_bolt
(float)Optional, Critical state line parameter m_par
(float)Optional, Yield surface constant (radius of yield surface in stress ratio space) F_sed
(float)Optional, Variable that controls the minimum value the reduction factor of the elastic moduli can get during reconsolidation p_sed
(float)Optional, Mean effective stress up to which reconsolidation strains are enhanced
The material formulations for the PM4Sand object are:
'PlaneStrain'
See als here
References
R.W.Boulanger, K.Ziotopoulou. âPM4Sand(Version 3.1): A Sand Plasticity Model for Earthquake Engineering Applicationsâ. Report No. UCD/CGM17/01 2017
StressDensityModelÂ¶

nDMaterial
('stressDensity', matTag, mDen, eNot, A, n, nu, a1, b1, a2, b2, a3, b3, fd, muNot, muCyc, sc, M, patm, *ssls, hsl, p1) This command is used to construct a multidimensional stress density material object for modeling sand behaviour following the work of Cubrinovski and Ishihara (1998a,b).
matTag
(int)integer tag identifying material mDen
(float)mass density eNot
(float)initial void ratio A
(float)constant for elastic shear modulus n
(float)pressure dependency exponent for elastic shear modulus nu
(float)Poissonâs ratio a1
(float)peak stress ratio coefficient (\(etaMax = a1 + b1*Is\)) b1
(float)peak stress ratio coefficient (\(etaMax = a1 + b1*Is\)) a2
(float)max shear modulus coefficient (\(Gn_max = a2 + b2*Is\)) b2
(float)max shear modulus coefficient (\(Gn_max = a2 + b2*Is\)) a3
(float)min shear modulus coefficient (\(Gn_min = a3 + b3*Is\)) b3
(float)min shear modulus coefficient (\(Gn_min = a3 + b3*Is\)) fd
(float)degradation constant muNot
(float)dilatancy coefficient (monotonic loading) muCyc
(float)dilatancy coefficient (cyclic loading) sc
(float)dilatancy strain M
(float)critical state stress ratio patm
(float)atmospheric pressure (in appropriate units) ssls
(list (float))void ratio of quasi steady state (QSSline) at pressures [pmin, 10kPa, 30kPa, 50kPa, 100kPa, 200kPa, 400kPa] (default = [0.877, 0.877, 0.873, 0.870, 0.860, 0.850, 0.833]) hsl
(float)void ratio of upper reference state (URline) for all pressures (default = 0.895) p1
(float)pressure corresponding to ssl1 (default = 1.0 kPa)
The material formulations for the StressDensityModel object are:
'ThreeDimensional'
'PlaneStrain'
References
Cubrinovski, M. and Ishihara K. (1998a) âModelling of sand behaviour based on state concept,â Soils and Foundations, 38(3), 115127.
Cubrinovski, M. and Ishihara K. (1998b) âState concept and modified elastoplasticity for sand modelling,â Soils and Foundations, 38(4), 213225.
Das, S. (2014) Three Dimensional Formulation for the StressStrainDilatancy ElastoPlastic Constitutive Model for Sand Under Cyclic Behaviour, Masterâs Thesis, University of Canterbury.
Tsinghua Sand ModelsÂ¶
CycLiqCPÂ¶

nDMaterial
('CycLiqCP', matTag, G0, kappa, h, Mfc, dre1, Mdc, dre2, rdr, alpha, dir, ein, rho) This command is used to construct a multidimensional material object that that follows the constitutive behavior of a cyclic elastoplasticity model for large post liquefaction deformation.
CycLiqCP material is a cyclic elastoplasticity model for large postliquefaction deformation, and is implemented using a cutting plane algorithm. The model is capable of reproducing small to large deformation in the pre to postliquefaction regime. The elastic moduli of the model are pressure dependent. The plasticity in the model is developed within the framework of bounding surface plasticity, with special consideration to the formulation of reversible and irreversible dilatancy.
The model does not take into consideration of the state of sand, and requires different parameters for sand under different densities and confining pressures. The surfaces (i.e. failure and maximum prestress) are considered as circles in the pi plane.
The model has been validated against VELACS centrifuge model tests and has used on numerous simulations of liquefaction related problems.
When this material is employed in regular solid elements (e.g., FourNodeQuad, Brick), it simulates drained soil response. When solidfluid coupled elements (up elements and SSP up elements) are used, the model is able to simulate undrained and partially drained behavior of soil.
matTag
(int)integer tag identifying material G0
(float)A constant related to elastic shear modulus kappa
(float)bulk modulus h
(float)Model parameter for plastic modulus Mfc
(float)Stress ratio at failure in triaxial compression dre1
(float)Coefficient for reversible dilatancy generation Mdc
(float)Stress ratio at which the reversible dilatancy sign changes dre2
(float)Coefficient for reversible dilatancy release rdr
(float)Reference shear strain length alpha
(float)Parameter controlling the decrease rate of irreversible dilatancy dir
(float)Coefficient for irreversible dilatancy potential ein
(float)Initial void ratio rho
(float)Saturated mass density
The material formulations for the CycLiqCP object are:
'ThreeDimensional'
'PlaneStrain'
See also here
CycLiqCPSPÂ¶

nDMaterial
('CycLiqCPSP', matTag, G0, kappa, h, M, dre1, dre2, rdr, alpha, dir, lambdac, ksi, e0, np, nd, ein, rho) This command is used to construct a multidimensional material object that that follows the constitutive behavior of a cyclic elastoplasticity model for large post liquefaction deformation.
CycLiqCPSP material is a constitutive model for sand with special considerations for cyclic behaviour and accumulation of large postliquefaction shear deformation, and is implemented using a cutting plane algorithm. The model: (1) achieves the simulation of postliquefaction shear deformation based on its physics, allowing the unified description of pre and postliquefaction behavior of sand; (2) directly links the cyclic mobility of sand with reversible and irreversible dilatancy, enabling the unified description of monotonic and cyclic loading; (3) introduces critical state soil mechanics concepts to achieve unified modelling of sand under different states.
The critical, maximum stress ratio and reversible dilatancy surfaces follow a rounded triangle in the pi plane similar to the MatsuokaNakai criterion.
When this material is employed in regular solid elements (e.g., FourNodeQuad, Brick), it simulates drained soil response. When solidfluid coupled elements (up elements and SSP up elements) are used, the model is able to simulate undrained and partially drained behavior of soil.
matTag
(int)integer tag identifying material G0
(float)A constant related to elastic shear modulus kappa
(float)bulk modulus h
(float)Model parameter for plastic modulus M
(float)Critical state stress ratio dre1
(float)Coefficient for reversible dilatancy generation dre2
(float)Coefficient for reversible dilatancy release rdr
(float)Reference shear strain length alpha
(float)Parameter controlling the decrease rate of irreversible dilatancy dir
(float)Coefficient for irreversible dilatancy potential lambdac
(float)Critical state constant ksi
(float)Critical state constant e0
(float)Void ratio at pc=0 np
(float)Material constant for peak mobilized stress ratio nd
(float)Material constant for reversible dilatancy generation stress ratio ein
(float)Initial void ratio rho
(float)Saturated mass density
The material formulations for the CycLiqCP object are:
'ThreeDimensional'
'PlaneStrain'
See also here
REFERENCES: Wang R., Zhang J.M., Wang G., 2014. A unified plasticity model for large postliquefaction shear deformation of sand. Computers and Geotechnics. 59, 5466.
Materials for Modeling Concrete WallsÂ¶
PlaneStressUserMaterialÂ¶

nDMaterial
('PlaneStressUserMaterial', matTag, nstatevs, nprops, fc, ft, fcu, epsc0, epscu, epstu, stc) This command is used to create the multidimensional concrete material model that is based on the damage mechanism and smeared crack model.
nstatevs
(int)number of state/history variables (usually 40) nprops
(int)number of material properties (usually 7) matTag
(int)integer tag identifying material fc
(float)concrete compressive strength at 28 days (positive) ft
(float)concrete tensile strength (positive) fcu
(float)concrete crushing strength (negative) epsc0
(float)concrete strain at maximum strength (negative) epscu
(float)concrete strain at crushing strength (negative) epstu
(float)ultimate tensile strain (positive) stc
(float)shear retention factor
PlateFromPlaneStressÂ¶

nDMaterial
('PlateFromPlaneStress', matTag, pre_def_matTag, OutofPlaneModulus) This command is used to create the multidimensional concrete material model that is based on the damage mechanism and smeared crack model.
matTag
(int)new integer tag identifying material deriving from predefined PlaneStress material pre_def_matTag
(int)integer tag identifying PlaneStress material OutofPlaneModulus
(float)shear modulus for out of plane stresses
PlateRebarÂ¶

nDMaterial
('PlateRebar', matTag, pre_def_matTag, sita) This command is used to create the multidimensional reinforcement material.
matTag
(int)new integer tag identifying material deriving from predefined uniaxial material pre_def_matTag
(int)integer tag identifying uniaxial material sita
(float)define the angle of reinforcement layer, 90 (longitudinal), 0 (tranverse)
PlasticDamageConcretePlaneStressÂ¶

nDMaterial
('PlasticDamageConcretePlaneStress', matTag, E, nu, ft, fc, <beta, Ap, An, Bn>) No documentation is available yet. If you have the manual, please let me know.
Contact Materials for 2D and 3DÂ¶
ContactMaterial2DÂ¶

nDMaterial
('ContactMaterial2D', matTag, mu, G, c, t) This command is used to construct a ContactMaterial2D nDMaterial object.
matTag
(int)integer tag identifying material mu
(float)interface frictional coefficient G
(float)interface stiffness parameter c
(float)interface cohesive intercept t
(float)interface tensile strength
The ContactMaterial2D nDMaterial defines the constitutive behavior of a frictional interface between two bodies in contact. The interface defined by this material object allows for sticking, frictional slip, and separation between the two bodies in a twodimensional analysis. A regularized Coulomb frictional law is assumed. Information on the theory behind this material can be found in, e.g. Wriggers (2002).
Note
 The ContactMaterial2D nDMaterial has been written to work with the SimpleContact2D and BeamContact2D element objects.
 There are no valid recorder queries for this material other than those which are listed with those elements
References:
Wriggers, P. (2002). Computational Contact Mechanics. John Wilely & Sons, Ltd, West Sussex, England.
ContactMaterial3DÂ¶

nDMaterial
('ContactMaterial3D', matTag, mu, G, c, t) This command is used to construct a ContactMaterial3D nDMaterial object.
matTag
(int)integer tag identifying material mu
(float)interface frictional coefficient G
(float)interface stiffness parameter c
(float)interface cohesive intercept t
(float)interface tensile strength
The ContactMaterial3D nDMaterial defines the constitutive behavior of a frictional interface between two bodies in contact. The interface defined by this material object allows for sticking, frictional slip, and separation between the two bodies in a threedimensional analysis. A regularized Coulomb frictional law is assumed. Information on the theory behind this material can be found in, e.g. Wriggers (2002).
Note
 The ContactMaterial3D nDMaterial has been written to work with the SimpleContact3D and BeamContact3D element objects.
 There are no valid recorder queries for this material other than those which are listed with those elements.
References:
Wriggers, P. (2002). Computational Contact Mechanics. John Wilely & Sons, Ltd, West Sussex, England.
Wrapper material for Initial State AnalysisÂ¶
InitialStateAnalysisWrapperÂ¶

nDMaterial
('InitialStateAnalysisWrapper', matTag, nDMatTag, nDim) The InitialStateAnalysisWrapper nDMaterial allows for the use of the InitialStateAnalysis command for setting initial conditions. The InitialStateAnalysisWrapper can be used with any nDMaterial. This material wrapper allows for the development of an initial stress field while maintaining the original geometry of the problem. An example analysis is provided below to demonstrate the use of this material wrapper object.
matTag
(int)integer tag identifying material nDMatTag
(int)the tag of the associated nDMaterial object nDim
(int)number of dimensions (2 for 2D, 3 for 3D)
Note
 There are no valid recorder queries for the InitialStateAnalysisWrapper.
 The InitialStateAnalysis off command removes all previously defined recorders. Two sets of recorders are needed if the results before and after this command are desired. See the example below for more.
 The InitialStateAnalysisWrapper material is somewhat tricky to use in dynamic analysis. Sometimes setting the displacement to zero appears to be interpreted as an initial displacement in subsequent steps, resulting in undesirable vibrations.
Initial Stress MaterialÂ¶

nDMaterial
('InitStressNDMaterial', matTag, otherTag, initStress, nDim) This command is used to construct an Initial Stress material object. The stressstrain behaviour for this material is defined by another material. Initial Stress Material enables definition of initial stress for the material under consideration. The strain that corresponds to the initial stress will be calculated from the other material.
matTag
(int)integer tag identifying material otherTag
(float)tag of the other material initStress
(float)initial stress nDim
(int)Number of dimensions (e.g. if plane strain nDim=2)
See also
Initial Strain MaterialÂ¶

nDMaterial
('InitStrainNDMaterial', matTag, otherTag, initStrain, nDim) This command is used to construct an Initial Strain material object. The stressstrain behaviour for this material is defined by another material. Initial Strain Material enables definition of initial strains for the material under consideration. The stress that corresponds to the initial strain will be calculated from the other material.
matTag
(int)integer tag identifying material otherTag
(int)tag of the other material initStrain
(float)initial strain nDim
(float)Number of dimensions
See also
UC San Diego soil modelsÂ¶
 PressureIndependMultiYield
 PressureDependMultiYield
 PressureDependMultiYield02
 PressureDependMultiYield03
PressureIndependMultiYieldÂ¶

nDMaterial
('PressureIndependMultiYield', matTag, nd, rho, refShearModul, refBulkModul, cohesi, peakShearStra, frictionAng=0., refPress=100., pressDependCoe=0., noYieldSurf=20, *yieldSurf) PressureIndependMultiYield material is an elasticplastic material in which plasticity exhibits only in the deviatoric stressstrain response. The volumetric stressstrain response is linearelastic and is independent of the deviatoric response. This material is implemented to simulate monotonic or cyclic response of materials whose shear behavior is insensitive to the confinement change. Such materials include, for example, organic soils or clay under fast (undrained) loading conditions.
matTag
(int)integer tag identifying material nd
(float)Number of dimensions, 2 for planestrain, and 3 for 3D analysis. rho
(float)Saturated soil mass density. refShearModul
(float)(\(G_r\)) Reference lowstrain shear modulus, specified at a reference mean effective confining pressure refPress of pâr (see below). refBulkModul
(float)(\(B_r\)) Reference bulk modulus, specified at a reference mean effective confining pressure refPress of pâr (see below). cohesi
(float)(\(c\)) Apparent cohesion at zero effective confinement. peakShearStra
(float)(\(\gamma_{max}\)) An octahedral shear strain at which the maximum shear strength is reached, specified at a reference mean effective confining pressure refPress of pâr (see below). frictionAng
(float)(\(phi\)) Friction angle at peak shear strength in degrees, optional (default is 0.0). refPress
(float)(\(p'_r\)) Reference mean effective confining pressure at which \(G_r\), \(B_r\), and \(\gamma_{max}\) are defined, optional (default is 100. kPa). pressDependCoe
(float)(\(d\)) A positive constant defining variations of \(G\) and \(B\) as a function of instantaneous effective confinement \(p'\) (default is 0.0)
\(G=G_r(\frac{p'}{p'_r})^d\)
\(B=B_r(\frac{p'}{p'_r})^d\)
If \(\phi=0\), \(d\) is reset to 0.0.
noYieldSurf
(float)Number of yield surfaces, optional (must be less than 40, default is 20). The surfaces are generated based on the hyperbolic relation defined in Note 2 below. yieldSurf
(list (float))Instead of automatic surfaces generation (Note 2), you can define yield surfaces directly based on desired shear modulus reduction curve. To do so, add a minus sign in front of noYieldSurf, then provide noYieldSurf pairs of shear strain (r) and modulus ratio (Gs) values. For example, to define 10 surfaces: yieldSurf = [r1, Gs1, âŠ, r10, Gs10]
See also notes
PressureDependMultiYieldÂ¶

nDMaterial
('PressureDependMultiYield', matTag, nd, rho, refShearModul, refBulkModul, frictionAng, peakShearStra, refPress, pressDependCoe, PTAng, contrac, *dilat, *liquefac, noYieldSurf=20.0, *yieldSurf=[], e=0.6, *params=[0.9, 0.02, 0.7, 101.0], c=0.3) PressureDependMultiYield material is an elasticplastic material for simulating the essential response characteristics of pressure sensitive soil materials under general loading conditions. Such characteristics include dilatancy (shearinduced volume contraction or dilation) and nonflow liquefaction (cyclic mobility), typically exhibited in sands or silts during monotonic or cyclic loading.
matTag
(int)integer tag identifying material nd
(float)Number of dimensions, 2 for planestrain, and 3 for 3D analysis. rho
(float)Saturated soil mass density.