Properties of Incremental Solutions for Dissipative Material

Abstract

Using the fully implicit rule for temporal integration, one may define a class of simple plasticity models, for which an incremental potential energy can be constructed. This potential has, in general, multiple stationary points, which correspond to equilibrium solutions when the material shows softening characteristics. Explicit expressions of the incremental potential energy are derived for von Mises plasticity with linear isotropic hardening within the context of a standard dissipative material. Using the Hill criterion for static stability, we show that stable incremental solutions are also (local) minimum points of the incremental potential energy for this particular material. Finite element results for this (simple) plasticity model are presented, which show that the stable solution also exhibits strong localization of plastic deformation.