This work is devoted to the derivation of improved bounds for the effective behavior of random linear elastic matrix-inclusions composites. In order to bounds their effective behavior, we present a new numerical approach, inspired by the works of Huet (J. Mech. Phys. Solids 1990 ; 38:813-41), which relies on the computation of the apparent behaviors associated to non square (or non cubic) volume elements (VEs) comprised of Voronoï cells assemblages, each cell being composed of a single inclusion surrounded by the matrix. Such non-square VEs forbid any direct application of boundary conditions to particles which is responsible for the artificial overestimation of the apparent behaviors observed for square VEs. By making used of the classical bounding theorems for linear elasticity and appropriate averaging procedures, new bounds are derived from ensemble averages of the apparent behavior associated with non square VEs. Their application to a two-phase composite composed of an isotropic matrix and aligned identical fibers randomly and isotropically distributed in the transverse plane leads to sharper bounds than those obtained by Huet. Then, by making use of this new numerical approach, a statistical study of the apparent behavior is carried out by means of Monte Carlo simulations. Subsequently, relying on the trends derived from this study, some proposals to define RVE criteria are presented.
