An adaptive least-squares mixed finite element method for elasto-plasticity

A least-squares mixed finite element method for the incremental formulation of elasto-plasticity using a plastic flow rule of von Mises type with isotropic hardening is presented. This approach is based on the use of the stress tensor, in addition to the displacement field, as independent process variables. The nonlinear least-squares functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based. For the finite element implementation under plane strain conditions, quadratic (i.e., next-to-lowest-order) Raviart-Thomas elements are used for the stress approximation, while the displacement is represented by standard quadratic conforming elements. Computational results for a benchmark problem of elasto-plasticity under plane strain conditions are presented in order to illustrate the effectiveness of the least-squares approach.