4.15.1.14. StressDensityModel¶
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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.