Drucker Prager

This command is used to construct an multi dimensional material object that has a Drucker-Prager yield criterium.

nDmaterial DruckerPrager $matTag $k $G $sigmaY $rho $rhoBar $Kinf $Ko $delta1 $delta2 $H $theta

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This Code has been Developed by: Peter Mackenzie, U Washington and the great Pedro Arduino, U Washington

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$matTag	integer tag identifying material
$k	bulk modulus
$G	shear modulus
$sigmaY	yield stress
$rho	frictional strength parameter
$rhoBar	non-associative parameter, 0 ≤ $rhoBar ≤ $rho
$Kinf	nonlinear isotropic strain hardening parameter, $Kinf ≥ 0
$Ko	nonlinear isotropic strain hardening parameter, $Ko ≥ 0
$delta1	nonlinear isotropic strain hardening parameter, $delta1 ≥ 0
$delta2	tension softening parameter, $delta2 ≥ 0
$H	linear kinematic strain hardening parameter, $H ≥ 0
$theta	controls relative proportions of isotropic and kinematic hardening, 0 ≤ $theta ≤ 1

The material formulations for the Drucker-Prager object are "ThreeDimensional," "PlaneStrain," "Plane Stress," "AxiSymmetric".

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EXAMPLE

An example like ZeroLengthContactNTS2D would be nice

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THEORY:

The theory for the Drucker-Prager yield criterion can be found at wikipedia here

The the nonlinear isotropic hardening term in the Drucker-Prager yield function is defined as

<math> K (\alpha_1) = \sigma_Y + \theta H \alpha + (K_{\infty} - K_o) \exp(-\delta_1 \alpha_1)</math>

The kinematic strain hardening is defined as

<math> H(\alpha_1) = (1 - \theta) H</math>

Tension softening is defined as

<math> T(\alpha_2) = T_o \exp(-\delta_2 \alpha_2)</math>

in which

<math> T_o = \sqrt{\frac{2}{3}} \frac{\sigma_Y}{\rho}</math>

defines the tension cutoff surface.

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REFERENCES;

Drucker, D. C. and Prager, W., "Soil mechanics and plastic analysis for limit design. Quarterly of Applied Mathematics, vol. 10, no. 2, pp. 157–165, 1952.