Effective response and field statistics in elasto-plastic and elasto-viscoplastic composites under radial and non-radial loadings

The aim of this study is to estimate as accurately as possible the effective response, as well as the statistics of the fields (first and second moments), in elasto-(visco) plastic heterogeneous materials with isotropic and/or kinematic hardening. After time-discretization, a new incremental variational principle for the increments in strain and internal variables in materials governed by two potentials is derived. This variational principle, together with the variational method of is used to introduce a linear comparison composite (LCC) at each time step, approximating in a variational sense the original problem. The effective response of the LCC, as well as the first and second moments of the stress and strain fields in each phase of the LCC are shown to provide estimates for the same quantities in the actual nonlinear elasto-(visco) plastic composite. The accuracy of the model is assessed by comparison with full-field simulations. The agreement is found to be quite satisfactory, in particular the asymmetry between tension and compression observed in elasto-plastic composites (Bauschinger effect) is well reproduced, unlike in other mean-field models. The statistics of the stress and strain fields, and to a certain extent, that of the back-stress field, are also in good agreement with full-field simulations.