Elastic moduli of composites with rigid sliding inclusions

We investigate the effect of interfaces on the elastic properties of composites with randomly distributed inclusions. Initially, the solution for a single isolated sliding inclusion is obtained and this result is used in two separate effective-medium theories, the self-consistent method and the differential scheme, to predict the elastic properties of composites containing a finite volume fraction of inclusions. For simplicity, the inclusions are assumed to be rigid. In the analysis, a parameter is introduced to describe the degree of sliding at the interface. Two limiting cases are perfect bonding and pure sliding at the inclusion-matrix interface. We show that the Poisson's ratio of the composite tends towards a universal value that is independent of the material parameters of the matrix, as the number of inclusions is increased. In contrast to the perfect-bonding case, both effective-medium theories give remarkably similar results in the pure-sliding limit.