Based on projection operators, an integral formulation is proposed for elastoviscoplastic heterogeneous materials. The problem requires a complete mechanical formulation, including the static equilibrium property concerning the known ®eld r, in addition to the classical ®eld equations concerning the unknown ®elds e and r. The formulation leads to an integral equation, in which elasticity and viscoplasticity effects interact through an homogeneous elastoviscoplastic medium with elastic moduli C and viscoplastic moduli B.To approximate the integral equation, the self-consistent scheme is followed. In order to obtain consistent approximation conditions, we introduce¯uctuations of elastic and viscoplastic strain rate ®elds with respect to known kinematically compatible ®elds. It results in a strain rate concentration relation connecting the strain rate at each point to the macroscopic loading conditions and the local stress ®eld. The results are presented and compared with other models and with experimental data in the case of a two-phase material.
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