Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. For this, we show that the geometric nonlinearities arising from the multiplicative decomposition of the strain can be controlled via polyconvexity and a priori stress bounds in terms of the energy density. While temporal oscillations are controlled via energy dissipation, the spatial compactness is obtained via regularizing terms involving gradients of the internal variables. Dedicated to Sir John Ball on the occasion of his 60th birthday.