4.15.1.15. StressDensityModel

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 multi-dimensional 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) Poisson’s 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 (QSS-line) 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 (UR-line) 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) ‘Modelling of sand behaviour based on state concept,’ Soils and Foundations, 38(3), 115-127.

Cubrinovski, M. and Ishihara K. (1998b) ‘State concept and modified elastoplasticity for sand modelling,’ Soils and Foundations, 38(4), 213-225.

Das, S. (2014) Three Dimensional Formulation for the Stress-Strain-Dilatancy Elasto-Plastic Constitutive Model for Sand Under Cyclic Behaviour, Master’s Thesis, University of Canterbury.