Homogenization of elastic-viscoplastic composites by the Mixed TFA

A new homogenization technique, based on the Transformation Field Analysis, able to determine the overall behavior of viscoplastic heterogeneous materials, is proposed. This method is derived developing a variational formulation of the compatibility and evolution equations governing two classical elastic-viscoplastic models, i.e. Perzyna and Perić models. A representation form for the stress field and the plastic multiplier is defined on the representative volume element (RVE) of the composite material, resulting in a significant reduction of the history variables ruling the evolution problem. A numerical procedure is developed integrating the evolution equation by a backward-Euler algorithm and solving the single time step developing a specific form of the predictor corrector technique. The accuracy of the proposed homogenization method is assessed through some numerical examples for elastic-viscoplastic composites. The applications aim to verify the effectiveness of the presented technique in modeling the elastic-viscoplastic composite behavior adopting a reduced number of history variables. The homogenization results are compared with the ones obtained by nonlinear finite element micromechanical analyses.