Towards mean-field potentials for elastoplastic composites

A formalism leading to mean-field potentials for random composites that account for elastic and plastic deformations concomitantly is elaborated. Deformations within constituent phases are described by archetypical potentials for rate-dependent elastoplasticity with combined isotropic and kinematical hardening. Plastic deformation fields are then additively decomposed into irrotational and solenoidal fields in such a way that variational approximations available for purely elastic and purely plastic potentials become applicative to elastoplastic potentials. The resulting mean-field potentials exhibit a generalized standard structure with a finite set of effective internal variables containing the phase averages of the irrotational and solenoidal fields. For simplicity, multi-phase composites are considered broadly but only a class of two-phase isotropic composites is considered thoroughly. Illustrative results are presented to highlight the role of these effective internal variables in elastoplastic transitions and residual stresses.