Homogenization of elasto-(visco) plastic composites based on an incremental variational principle

An original approach is proposed in order to compute the homogenized response of composite materials with elasto-(visco) plastic constituents. The formulation is based on an incremental variational principle according to which the local stress–strain relation derives from a single incremental potential constructed from a free energy and a dissipation function. Both rate-dependent and rate-independent plasticity are handled within the same framework through the choice of the dissipation function. The key feature of the model is the explicit use of the elastic trial strain in order to define a Linear Comparison Composite whose mechanical response coincides with the response of the actual composite at a given time step. The hereditary character of the behavior is accounted for through internal variables. The method was successfully applied to several two-phase elasto-plastic and elasto-viscoplastic composites made of a continuous matrix reinforced by ellipsoidal inclusions. General loading conditions, including cyclic ones, were considered. The proposed method provides accurate predictions of the macroscopic response in many cases, and competes with previously proposed schemes in elasto-(visco) plasticity.