Effective elasto-plastic properties of inclusion-reinforced composites. Study of shape, orientation and cyclic response

A Hill-type incremental formulation for two-phase composites was recently proposed by Doghri and Ouaar [Int. J. Solids Struct. 40(7) (2003) 1681]. We present a slightly improved version of the formulation and test it for non-spherical inclusions. The formulation enables the simulation of unloading and cyclic loadings. Two homogenization schemes are implemented: Mori-Tanaka (M-T) and an interpolative double-inclusion model (D-I). Two plasticity models which can be used for any phase are implemented: classical J2 elasto-plasticity and Chaboche's model with non-linear kinematic and isotropic hardenings. All rate equations are discretized in time using implicit generalized mid-point schemes. A two-scale procedure for the simulation of composite structures is developed: a finite element (FE) program at macro-scale linked to the homogenization module at micro-scale. An extensive validation of the homogenization predictions against experimental data and direct unit cell FE simulations is conducted for several composite systems.