The determination of the behavior of heterogeneous materials with complex physical and mechanical couplings constitutes a challenge in the design of new materials and the modeling of their effective properties. In real inhomogeneous materials, the simultaneous presence of elastic mechanisms and non linear inelastic ones (viscoplastic, magnetic, ferroelectric, shape memory effect etc.) leads to a complex non linear coupling between the mechanical fields which is tricky to represent in a simple and efficient way. Hence, for many situations the effective global behavior does not follow the same structure than the local constitutive one. Regarding space-time couplings for instance, a heterogeneous material composed of phases described by Maxwell elements can not be considered as a Maxwellian solid at the macro scale.
In this paper, we introduce a new micro-macro approach based on translated fields in its generalized form to be applied to different coupled phenomena. The local total strain (rate) is composed additively of an elastic strain (rate) and an inelastic one which is no more limited to be “stress free” as considered originally by Kröner. An extended (non conventional) self-consistent model is then proposed starting from the integral equation for a translated strain (rate) field and using the projection operators algebra introduced by Kunin. The chosen translated field is the compatible inelastic strain (rate) of the fictitious inelastic heterogeneous medium submitted to a uniform unknown boundary condition. The self-consistency condition amounts to define analytically these boundary conditions so that a relative simple and compact strain (rate) concentration equation is obtained.
In order to illustrate the method, the case of a non linear elastic-viscoplastic coupling is developed and applied to different classes of composites and polycrystals.