Four Node Quad u-p Element

FourNodeQuadUP is a four-node plane-strain element using bilinear isoparametric formulation. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot’s theory of porous medium. Each element node has 3 degrees-of-freedom (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 counter-clockwise 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