An efficient solution algorithm for elastoplasticity and its first implementation towards uniform h- and p- mesh refinements

The main subject of this paper is the detailed description of an algorithm solving elastoplastic deformations. Our concern is a one time-step problem, for which the minimization of a convex but non-smooth functional is required. We propose a minimization algorithm based on the reduction of the functional to a quadratic functional in the displacement and the plastic strain increment omitting a certain nonlinear dependency. The algorithm also allows for an easy extension to higher order finite elements. A numerical example in 2D reports on first results for uniform hand pmesh refinements.