Symplectic bipotentials

Mathematics and Mechanics of Solids

Abstract

In a previous paper, we proposed a symplectic version of the Brezis–Ekeland–Nayroles principle based on the concepts of Hamiltonian inclusions and symplectic polar functions. We applied it to the standard plasticity. The object of this work is to extend the previous formalism to non-associated plasticity. For this aim, we generalize the concept of bipotential to dynamical systems. The keystone idea is to define a symplectic bipotential. We present a method to build it from a bipotential. Next, we generalize the symplectic Brezis–Ekeland–Nayroles principle to the non-associated dissipative laws. We apply it to the non-associated plasticity and to the unilateral contact law with Coulomb’s dry friction.

Authors 2

1. Michael Ban Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen, Germany

2. G. de Saxcé corresponding

   Centre National de la Recherche Scientifique · Université de Lille · Centrale Lille Institut · Laboratoire de Mécanique, Multiphysique, Multiéchelle

   Affiliation as printed

   Univ. Lille, CNRS, Centrale Lille, UMR 9013 – LaMcube, Laboratoire de mécanique multiphysique multiéchelle, Lille, France