Rate-Independent elastoplasticity at finite strain and its numerical approximation

Abstract

Gradient plasticity at large strains with kinematic hardening is analyzed as qua-sistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the dissipation are approximated numerically by finite elements and implicit time discretization, such that a computationally imple-mentable scheme is obtained. The non-selfpenetration as well as a possible friction-less unilateral contact is considered and approximated numerically by a suitable penalization method which keeps polyconvexity and simultaneously bypasses the Lavrentiev phenomenon. The main result concerns the convergence of the numerical scheme towards energetic solutions. In the case of incompressible plasticity and of nonsimple materials, where the energy depends on the second derivative of the deformation, we derive an explicit stability criterion for convergence relating the spatial discretization and the penalizations.