Micromechanics-based multi-site modeling of elastoplastic behavior of composite materials

The Multi-Site Mori-Tanaka (MSMT) scheme is used to derive the macroscopic response of elastoplastic composites with ordered microstructures. The key point of the multi-site modeling remains the derivation of the interactions between inclusions and their neighborhood through the multi-site interaction tensor. The micromechanics formalism is based on the ellipsoidal Eshelby's inclusion concept. The kinematic integral equation of Dederichs and Zeller (1973) is used as formal solution of the heterogeneous material problem. This enables the computation of the interaction between one inclusion and its neighbors and thus for a cluster of inclusions arranged according to a cubic lattice. Such a mean-field scheme is coupled with the well-known Hill-type incremental formulation for the nonlinear behavior. The J2 elasto-plasticity is derived in which the consistent (or algorithmic) modulus of each phase is computed following the work of Doghri and Ouaar (2003). Numerical results are obtained considering heterogeneous materials such as Metal Matrix Composites (MMCs) as well as Particle-reinforced MMCs (PRMMCs). Systematic analysis of various micro-parameters (volume fraction, morphological and topological parameters) are considered. The model predictions are compared with Finite Elements solutions and experimental data as well as recent variational formulations provided from the open literature.