Stress Density Material

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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).

nDMaterial StressDensityModel $matTag $mDen $eNot $A $n $nu $a1 $b1 $a2 $b2 $a3 $b3 $fd $muNot $muCyc $sc $M $patm <$ssl1 $ssl2 $ssl3 $ssl4 $ssl5 $ssl6 $ssl7 $ssl8 $ssl9 $ssl10 $hsl $p1 $p2 $p3 $p4 $p5 $p6 $p7 $p8 $p9 $p10>

$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 (Gn_max = a2 + b2*Is)
$b2	max shear modulus coefficient (Gn_max = a2 + b2*Is)
$a3	min shear modulus coefficient (Gn_min = a3 + b3*Is)
$b3	min shear modulus coefficient (Gn_min = 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)

Optional steady state line parameters (default values shown for each, be careful with units)

<$ssl1>	void ratio of quasi steady state (QSS-line) at pressure $p1 (default = 0.877)
<$ssl2>	void ratio of quasi steady state (QSS-line) at pressure $p2 (default = 0.877)
<$ssl3>	void ratio of quasi steady state (QSS-line) at pressure $p3 (default = 0.873)
<$ssl4>	void ratio of quasi steady state (QSS-line) at pressure $p4 (default = 0.870)
<$ssl5>	void ratio of quasi steady state (QSS-line) at pressure $p5 (default = 0.860)
<$ssl6>	void ratio of quasi steady state (QSS-line) at pressure $p6 (default = 0.850)
<$ssl7>	void ratio of quasi steady state (QSS-line) at pressure $p7 (default = 0.833)
<$ssl8>	void ratio of quasi steady state (QSS-line) at pressure $p8 (default = 0.833)
<$ssl9>	void ratio of quasi steady state (QSS-line) at pressure $p9 (default = 0.833)
<$ssl10>	void ratio of quasi steady state (QSS-line) at pressure $p10 (default = 0.833)
<$hsl>	void ratio of upper reference state (UR-line) for all pressures (default = 0.895)
<$p1>	pressure corresponding to $ssl1 (default = 1.0 kPa)
<$p2>	pressure corresponding to $ssl1 (default = 10.0 kPa)
<$p3>	pressure corresponding to $ssl1 (default = 30.0 kPa)
<$p4>	pressure corresponding to $ssl1 (default = 50.0 kPa)
<$p5>	pressure corresponding to $ssl1 (default = 100.0 kPa)
<$p6>	pressure corresponding to $ssl1 (default = 200.0 kPa)
<$p7>	pressure corresponding to $ssl1 (default = 400.0 kPa)
<$p8>	pressure corresponding to $ssl1 (default = 400.0 kPa)
<$p9>	pressure corresponding to $ssl1 (default = 400.0 kPa)
<$p10>	pressure corresponding to $ssl1 (default = 400.0 kPa)

The material formulations for the StressDensity object are "ThreeDimensional" and "PlaneStrain"

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Code Developed by Saumyashuchi Das, University of Canterbury. Maintained by Chris McGann

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General Information

This nDMaterial object provides the stress density model for sands under monotonic and cyclic loading as set forth by Cubrinovski and Ishihara (1998a,b). The original formulation for this model was applicable to plane strain conditions. The current implementation also includes the extension for consideration of 3D conditions by Das (2014).

Usage Examples

The following usage example provides the input parameters for dry pluviated Toyura sand (with initial void ratio e = 0.73) after Cubrinovski and Ishihara (1998b). The units of this analysis are Mg, kN, s, and m.

# mass density
set mDen  1.8
# atmospheric pressure
set patm  98.1
# stress density model parameters
set eNot  0.730
set A     250.0
set n     0.60
set a1    0.58
set b1    0.023
set a2    230.0
set b2    65.0
set a3    79.0
set b3    16.0
set fd    4.0
set muNot 0.22
set muCyc 0.0
set sc    0.0055
set M     0.607
nDMaterial StressDensityModel 1  $mDen $eNot $A $n $nu $a1 $b1 $a2 $b2 $a3 $b3 $fd $muNot $ muCyc $sc $M $patm

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.

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