11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. O˜ nate, J. Oliver and A. Huerta (Eds) COARSE–GRAINING APPROACHES FOR PARTICULATE COMPOSITES AS MICROPOLAR CONTINUA Patrizia Trovalusci * , Maria Laura De Bellis * , Agnese Murrali * and Martin Ostoja-Starzewski † * Department of Structural and Geotechnical Engineering, Sapienza, University of Rome, Italy e-mail: patrizia.trovalusci@uniroma1.it † Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana–Champaign,USA Key words: Random composites, Cosserat continua, statistical homogenization, Repre- sentative Volume Element. Abstract. 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 ac- tual microstructure of a two–dimensional and two–phase random medium and to estimate the elastic moduli of the energy equivalent homogeneous micropolar continuum. This pro- cedure 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. 1 INTRODUCTION Several composite materials, extensively adopted in many engineering fields, are char- acterized by particulate random microstructures. Examples are polymer, ceramic, metal matrix composites or also concrete, granular materials and porous rocks (Figure 1). A key issue in mechanics of materials characterized by microstructural randomness is that the classical concept of the Representative Volume Element (RVE), well estab- lished in periodicity based homogenization techniques since many years [16, 9], loses its validity [11]. In the last few years, various procedures based on the solution of specific Boundary Value Problems (BVPs) have been proposed to perform classical homogeniza- tion for non–periodic assemblies [17, 3, 14, 1, 15]. In order to account for the effects of 1