Multigrid methods for Prandtl-Reuss plasticity

We explain an interface for the implementation of rate-independent elastoplasticity which separates the pointwise evaluation of the elastoplastic material law and the global solution of the momentum balance equation. The elastoplastic problem is discretized in time by diagonally implicit Runge-Kutta methods and every time step is solved with a Newton iteration. For the discretization in space the material parameters are computed at the Gauß points which are used for the numerical integration. The displacement vector is approximated with stabilized finite elements. The assembling of the linearized problem uses an abstract interface for the material description only. The linear problem in every Newton step is solved with an adaptive, parallel multigrid method. We present a detailed numerical investigation of a benchmark example for perfect plasticity and isotropic hardening.