QUASISTATIC EVOLUTION IN PERFECT PLASTICITY FOR GENERAL HETEROGENEOUS MATERIALS

Abstract. Inspired by some recents developments in the theory of small-strain heterogeneous elastoplasticity, we both revisit and generalize the formulation of the quasistatic evolutionary prob-lem in perfect plasticity given by Francfort and Giacomini in [10]. We show that their definition of the plastic dissipation measure is equivalent to an abstract one, where it is defined as the supre-mum of the dualities between the deviatoric parts of admissible stress fields and the plastic strains. By means of this abstract definition, a viscoplastic approximation and variational techniques from the theory of rate-independent processes give the existence of an evolution satisfying an energy-dissipation balance and consequently Hill’s maximum plastic work principle for an abstract and very large class of yield conditions. 1