An incremental variational formulation for the prediction of the effective work-hardening behavior and field statistics of elasto-(visco)plastic composites

A new nonlinear and variational homogenization procedure that incorporates the fluctuations of the plastic strains within the phases is proposed to assess the local and effective responses of elasto-(visco)plastic composites with local work-hardening. The formulation is an extension of the EIV approach of Lahellec and Suquet (2007a) initially proposed for elasto-viscoplastic composites without both threshold and hardening. This extension relies both on an appropriate linearization of the stored-energy function which accounts for the isotropic and kinematic hardening and an incorporation of the elastic unloading. The accuracy of the approach is then assessed by comparisons with reference numerical solutions and other nonlinear homogenization schemes of the literature carried out on both porous elasto-plastic materials and several reinforced elasto-(visco)plastic composites subjected to cyclic proportional loadings.