Variational formulations for the plane strain elastic-plastic problem for materials governed by the von Mises criterion

Path-dependent materials, complying with Drucker's postulate requirements and governed by an internal variable rate plasticity model, are considered. A variational principle for the small strain, rate plasticity problem is established in this context and extended to cover finite loading steps. Results are subsequently specialized to plane strain solids made of elastically isotropic materials with a plastic behavior governed by the von Mises criterion, accounting for combined isotropic and kinematic hardening. By exploiting previous results, the formulation is fully reduced to the plane. Further generalizations of the statements are also provided, which can be regarded as extensions to the elastic-plastic, plane strain problem of the Hu-Washizu principle in elasticity.