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

Nelly Point; Silvano Erlicher

doi:10.3934/dcdss.2013.6.567

Article Contents

2013, Volume 6, Issue 2: 567-590. Doi: 10.3934/dcdss.2013.6.567

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

Nelly Point^1, and
Silvano Erlicher^2,

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

Received: June 30, 2011

Revised: November 30, 2011

Published: March 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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