Compatible mixed formulations for elastoplastic models (Q1371510)

We consider two approximate mixed variational formulations for an elastoplastic model with mixed hardening. In particular, we address a three-field minimum principle in displacements, plastic strains and kinematic internal variables, and a five-field minimum principle in displacements, total and plastic strains, stresses and kinematic internal variables. The matrix formulation used in this paper avoids some of the compatibility conditions as well as the Prager's criterion to define the stress and strain vectors. Moreover, it is shown that the plastic multiplier is not a state variable of the two approximate problems, and the variationally consistent plastic flow rule can be expressed in terms of the subdifferential of the dissipation functional.