Coarse-graining approaches for particulate composites as micropolar continua

A multitude of composite materials ranging from polycrystals up to concrete and masonry–like materials overwhelmingly display random morphologies. In this work we propose a statistically–based multiscale procedure which allow us to simulate the actual microstructure of a two–dimensional and two–phase random medium and to estimate the elastic moduli of the energy equivalent homogeneous micropolar continuum. This procedure uses finite–size scaling of Statistical Volume Elements (SVEs) and approaches the so–called Representative Volume Element (RVE) through two hierarchies of constitutive bounds, respectively stemming from the numerical solution of Dirichlet and Neumann non-classical boundary value problems, set up on mesoscale material cells. The results of the performed numerical simulations point out the worthiness of accounting spatial randomness as well as the additional degrees of freedom of the Cosserat continuum.