Finite element analysis and algorithms for single-crystal strain-gradient plasticity

We provide optimal a priori estimates for finite element approximations of a model of rate-independent single-crystal strain-gradient plasticity. The weak formulation of the problem takes the form of a variational inequality in which the primary unknowns are the displacement and slips on the prescribed slip systems, as well as the back-stress associated with the vectorial microstress. It is shown that the return mapping algorithm for local plasticity can be applied element-wise to this non-local setting. Some numerical examples illustrate characteristic features of the non-local model.