Effect of overlapping inclusions on effective elastic properties of composites

We are considering, in this study, to quantify the difference between two morphologies: heterogeneous materials with overlapping identical spherical inclusions and heterogeneous materials with identical hard one. Coupling with numerical simulations, the statistical analysis of microstructures morphology was used to evaluate the representativeness of results. The methodology, developed in Kanit et al. (2003), is used to determine exactly the integral range (IR), variance and covariance of each microstructure type. The obtained results show that the integral range of microstructures with hard spheres, is simply, the volume of one inclusion in the deterministic representative volume element, and for microstructures with overlapping spheres, is 8 times the integral range in the case of hard spheres. The obtained results suggest us to define a new concept what we propose to name the Equivalent Morphology Concept (EMC). The relationships between parameters of two microstructures are presented.