# American Institute of Mathematical Sciences

April  2013, 6(2): 567-590. doi: 10.3934/dcdss.2013.6.567

## Pseudo-potentials and bipotential: A constructive procedure for non-associated plasticity and unilateral contact

 1 Conservatoire National des Arts et Métiers CNAM, 292 rue Saint-Martin, Département de Mathématiques (442), 75141 Paris, Cedex 03, France 2 Direction Technique et Scientifique, EGIS Industries, 4, rue Dolores Ibarruri, 93188 Montreuil Cedex, France

Received  July 2011 Revised  December 2011 Published  November 2012

Pseudo-potentials are very useful tools to define thermodynamically admissible constitutive rules. Bipotentials are convenient for numerical purposes, in particular for non-associative rules. Unfortunately, these functionals are not always easy to construct starting from a given constitutive law. This work proposes a procedure to find the pseudo-potentials and the bipotential starting from the usual description of a non-associative constitutive law. This method is applied to different non-associative plasticity models such as the Drucker-Prager model and the non-linear kinematic hardening model. The same procedure allows one to obtain the pseudo-potentials of an endochronic plasticity model. The pseudo-potentials for the contact problem with dissipation are constructed using the same ideas. For all these non-associative constitutive laws a bipotential is then automatically deduced.
Citation: Nelly Point, Silvano Erlicher. Pseudo-potentials and bipotential: A constructive procedure for non-associated plasticity and unilateral contact. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 567-590. doi: 10.3934/dcdss.2013.6.567
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