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 |
integer tag identifying material |
mDen |
mass density |
eNot |
initial void ratio |
A |
constant for elastic shear modulus |
n |
pressure dependency exponent for elastic shear modulus |
nu |
Poisson's ratio |
a1 |
peak stress ratio coefficient (etaMax = a1 + b1 * Is) |
b1 |
peak stress ratio coefficient (etaMax = a1 + b1 * Is) |
a2 |
max shear modulus coefficient (Gnmax = a2 + b2 * Is) |
b2 |
max shear modulus coefficient (Gnmax = a2 + b2 * Is) |
a3 |
min shear modulus coefficient (Gnmin = a3 + b3 * Is) |
b3 |
min shear modulus coefficient (Gnmin = a3 + b3 * Is) |
fd |
degradation constant |
muNot |
dilatancy coefficient (monotonic loading) |
muCyc |
dilatancy coefficient (cyclic loading) |
sc |
dilatancy strain |
M |
critical state stress ratio |
patm |
atmospheric pressure (in appropriate units) |
|
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]) |
|
void ratio of upper reference state (UR-line) for all pressures (default = 0.895) |
p1 |
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.