A Statistically-Based Homogenization Approach for Particle Random Composites as Micropolar Continua

This article is focused on the identification of the size of the representative volume element (RVE) and the estimation of the relevant effective elastic moduli for particulate random composites modeled as micropolar continua. To this aim, a statistically-based scale-dependent multiscale procedure is adopted, resorting to a homogenization approach consistent with a generalized Hill's type macrohomogeneity condition. At the fine level the material has two phases (inclusions/matrix). Two different cases of inclusions, either stiffer or softer than the matrix, are considered. By increasing the scale factor, between the size of intermediate control volume elements (Statistical Volume Elements, SVEs) and the inclusions size, series of boundary value problems are numerically solved and hierarchies of macroscopic elastic moduli are derived. The constitutive relations obtained are grossly isotropic and are represented in terms of classical bulk, shear and micropolar bending moduli. The "finite size scaling" of these relevant elastic moduli for the two different material contrasts (ratio of inclusion to matrix moduli) is reported. It is shown that regardless the scaling behavior, which depends on the material phase contrast, the RVE size is statistically detected. The results of the performed numerical simulations also highlight the importance of taking into account the spatial randomness of inclusions which intersect the SVEs boundary.