Particulate random composites homogenized as micropolar materials

Many composite materials, widely used in different engineering fields, are characterized by random distributions of the constituents. Examples range from polycrystals to concrete and masonry-like materials. In this work we propose a statistically-based scale-dependent multiscale procedure aimed at the simulation of the mechanical behavior of a two-phase particle random medium and at the estimation of the elastic moduli of the energy-equivalent homogeneous micropolar continuum. The key idea of the procedure is to approach the so-called Representative Volume Element (RVE) using finite-size scaling of Statistical Volume Elements (SVEs). To this end properly defined Dirichlet, Neumann, and periodic-type non-classical boundary value problems are numerically solved on the SVEs defining hierarchies of constitutive bounds. The results of the performed numerical simulations point out the importance of accounting for spatial randomness as well as the additional degrees of freedom of the continuum with rigid local structure.