Estimates for the overall linear properties of pointwise heterogeneous solids with application to elasto-viscoplasticity

New estimates are derived for the overall properties of linear solids with pointwise heterogeneous local properties. The derivation relies on the use of 'comparison solids' which, unlike comparison solids considered previously, are themselves pointwise heterogeneous. The estimates are then exploited within an incremental homogenization scheme to determine the overall response of multiphase elasto-viscoplastic solids under arbitrary loading histories. By way of example, the scheme is applied to incompressible Maxwellian solids with power-law plastic dissipation; particularly simple estimates of the Hashin-Shtrikman type are obtained. Predictions are confronted with full-field simulations for particulate composites under cyclic and rotating loading conditions. Good agreement is found for all cases considered. In particular, elasto-plastic transitions, tension-compression asymmetries (Bauschinger effect) and stress-path distortions induced by material heterogeneity are all well-captured, thus improving significantly on commonly used elastic-plastic decoupled schemes.