Micromechanically established constitutive equations for multiphase materials with viscoelastic-viscoplastic phases

A model for viscoelastic-viscoplastic solids is incorporated in a micromechanical analysis of composites with periodic microstructures in order to establish closed-form coupled constitutive relations for viscoelastic- viscoplastic multiphase materials. This is achieved by employing the homogenization technique for the establishment of concentration tensors that relate the local elastic and inelastic fields to the externally applied loading. The resulting constitutive equations are sufficiently general such that viscoelastic, viscoplastic and perfectly elastic phases are obtained as special cases by a proper selection of the material parameters the phase. Results show that the viscoelastic and viscoplastic mechanisms have significant effect on the global stress-strain, relaxation and creep behavior of the composite, and that its response is strongly rate-dependent in the reversible and irreversible regimes.