Periodic homogenization and damage evolution in RVE composite material with inclusion

This work deals with the coupling between a periodic homogenization procedure and a damage process occurring in a RVE of inclusion composite materials. We mainly seek on the one hand to determine the effective mechanical properties according to the different volume fractions and forms of inclusions for a composite with inclusions at the macroscopic level, and on the other hand to explore the rupture mechanisms that can take place at the microstructure level. To do this; the first step is to propose a periodic homogenization procedure to predict the homogenized mechanical characteristics of an inclusion composite. This homogenization procedure is applied to the theory based on finite element analysis by the Abaqus calculation code. The inclusions are modeled by a random object modeler, and the periodic homogenization method is implemented by python scripts. It is then a matter of introducing the damage into the problem of homogenization, that is to say; once the homogenized characteristics are assessed in the absence of the damage initiated by microcracks and micro cavitations, it is then possible to introduce damage models by a subroutine (Umat) in the Abaqus calculation code. The verifications carried out focused on RVE of composite materials with inclusions.