Drucker Prager: Difference between revisions
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| '''$H ''' || linear kinematic strain hardening parameter | | '''$H ''' || linear kinematic strain hardening parameter | ||
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| '''$theta ''' || | | '''$theta ''' || strain hardening proportion parameter | ||
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The theory for the Drucker-Prager yield criterion can be found at wikipedia [http://en.wikipedia.org/wiki/Drucker_Prager_yield_criterion here] | The theory for the Drucker-Prager yield criterion can be found at wikipedia [http://en.wikipedia.org/wiki/Drucker_Prager_yield_criterion here] | ||
The the isotropic hardening | The the nonlinear isotropic hardening term in the Drucker-Prager yield function is defined as | ||
<math> K | <math> K (\alpha_1) = \sigma_Y + \theta H \alpha + (K_{\infty} - K_o) \exp(-\delta_1 \alpha_1)</math> | ||
</math> | |||
The kinematic strain hardening is defined as | |||
<math> H | <math> H(\alpha_1) = (1 - \theta) H</math> | ||
</math> | |||
Tension softening is defined as | Tension softening is defined as | ||
<math> T (\alpha_2) = T_o \exp(-\delta_2 \alpha_2) | <math> T(\alpha_2) = T_o \exp(-\delta_2 \alpha_2)</math> | ||
</math> | |||
in which | in which | ||
<math> T_o = \sqrt{\frac{2}{3}} \frac{\sigma_Y}{\rho} | <math> T_o = \sqrt{\frac{2}{3}} \frac{\sigma_Y}{\rho}</math> | ||
</math> | |||
defines the tension cutoff surface. | defines the tension cutoff surface. | ||
Revision as of 01:17, 2 February 2010
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 |
This Code has been Developed by: Peter Mackenzie, U Washington and the great Pedro Arduino, U Washington
| $matTag | integer tag identifying material |
| $k | bulk modulus |
| $G | shear modulus |
| $sigmaY | yield stress |
| $rho | frictional strength parameter |
| $rhoBar | non-associative parameter |
| $Kinf | nonlinear isotropic strain hardening parameter |
| $Ko | nonlinear isotropic strain hardening parameter |
| $delta1 | nonlinear isotropic strain hardening parameter |
| $delta2 | tension softening parameter |
| $H | linear kinematic strain hardening parameter |
| $theta | strain hardening proportion parameter |
The material formulations for the Drucker-Prager object are "ThreeDimensional," "PlaneStrain," "Plane Stress," "AxiSymmetric".
EXAMPLE
An example like ZeroLengthContactNTS2D would be nice
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.
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.