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 Representative Volume Element (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. 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