The purpose of this study is to determine the mechanical characteristics for inclusion composite materials by several homogenization methods. Firstly, it involves modeling the (RVE) using the semi-analytical homogenization method, then formulating and implementing a periodic homogenization technique, where we proposed introducing additional degrees of freedom supporting the components of macroscopic deformations applying at composite “Concrete”. It is necessary to introduce behavior laws and damage models for composite materials. For this, we develop damage expressions based on material behavior models in order to analyze local fields and introduce failure criteria. Simulation by the semi-analytical Mori-Tanaka model gives good results for a two-phase material when the heterogeneity concentration is less than 30%. And as for modeling by the proposed periodic homogenization method, it gives us very satisfactory results regarding the prediction of the effective mechanical characteristics of composite materials. The percentage of inclusions as well as their shape have an influence on the latter. A parametric study was carried out to determine the influence of variations in the mechanical properties of mortar on those of effective “concrete” composite. The damage models developed allowed us to reproduce the softening behavior of the composite materials, which is progressively reduced as microcracks develop.
Benyahi et al. (Wed,) studied this question.