Complementary formulation of the TFA for the elasto-plastic analysis of composites

In this paper, a new mixed nonuniform Transformation Field Analysis (TFA) homogenization technique for deriving the overall mechanical response of heterogeneous materials is proposed. The new TFA approach is based on a mixed stress variational formulation of the elasto-plasticity theory, assuming stresses and plastic multiplier as independent variables. The case of periodic composites is considered, so that the homogenization is performed on a repetitive unit cell that plays the equivalent role of representative volume element for random media. The unit cell of the material is divided into subsets and in each subset the weak form of the compatibility condition and of the consistency condition are enforced, leading to a simultaneous evaluation of the stress and of the plastic strain field. It is assumed that the stress field satisfies a priori the equilibrium equations while the inelastic strain distribution is evaluated as function of the assumed stress resulting nonuniform in each subset. Some numerical examples are performed in the framework of plane stress plasticity in order to assess the effectiveness of the proposed technique. In particular, the homogenization results are compared with the ones carried out by micromechanical nonlinear finite element analyses.