Error indicators and mesh refinements for finite-element-computations of elastoplastic deformations

Many interesting tasks in technology need the solution of complex boundary value problems within the mathematical theory of elastoplasticity. Error controlled adaptive strategies should be used in order to achieve a prescribed accuracy of the computed solutions at minimum cost. Local error indicators in the primal form of the finite-element-method for Hencky- and Prandtl–Reusplasticity without and with nonlinear hardening are presented, controlling global errors of equilibrium, plastic strain rates, the yield condition and the numerical integration of the flow rule. A 2D finite element code was extended for the transfer of physical parameters between meshes and for a combined space and time adaptive strategy. All error indicators are tested with the benchmark example of a rectangular plane strain problem with a hole.