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

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.