Existence of minimizers in incremental elasto-plasticity with finite strains

We consider elasto-plastic deformations of a body which is subjected to a time-dependent loading. The model includes fully nonlinear elasticity as well as the multiplicative split of the deformation gradient into an elastic part and a plastic part. Using the energetic formulation for this rate-independent process we derive a time-incremental problem, which is a minimization problem with respect to the deformation and the plastic variables. We provide assumptions on the constitutive laws of the material which guarantee that the incremental problem can be solved for as many time steps as desired. The methods relies on the polyconvexity of the so-called condensed energy functional and on a priori estimates for the plastic variables using the dissipation distance.