Scale and boundary conditions effects in elasticity and damage mechanics of random composites

Spatial randomness, as opposed to periodic geometries, may have a significant effect on damage formation in composite materials. This issue was studied extensively over the last few years [1, 2, 3, 4], and in this paper we report new results on effects of scale and boundary conditions in the determination of meso-scale continuum-type models for elasticity and fracture. These models are formulated on scales larger than the single inclusion, yet smaller than the conventional continuum limit. The latter corresponds to the classical concept of aRepresentative Volume Element (RVE) which presupposes the presence representation of the microstructure with all the typical microheterogeneities, and thus calls for relatively large volumes. Indeed, according to Hill [5], an RVE should be such that the relations between volume average stress and strain should be the same regardless of whether kinematic or stress boundary conditions have been used.