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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. Copyright © 2012 John Wiley & Sons, Ltd.