A Prange-Hellinger-Reissner type finite element formulation for small strain elasto-plasticity

In this contribution we propose a mixed variational formulation of the Prange-Hellinger-Reissner type for elasto-plasticity at small strains. Here, the displacements and the stresses are interpolated independently, which are balanced within the variational functional by the relation of the elastic strains and the partial derivative of the complementary stored energy with respect to the stresses. For the elasto-plastic material behavior a von Mises yield criterion is considered, where we restrict ourselves w.l.o.g. to linear isotropic hardening. In the proposed formulation we enforce the constraints arising from plasticity point-wise in contrast to the element-wise realization of the plastic return mapping algorithm suggested in Simo et al. (1989). The performance of the new formulation is demonstrated by the analysis of several benchmark problems. Here, we compare the point-wise treatment of elasto-plasticity with the original element-wise formulation of Simo et al. (1989). Furthermore, we derive an algorithmic consistent treatment for plane stress as well as for plane strain condition.