Elastic interactions in particulate composites with perfect as well as imperfect interfaces

We describe a method for computing interactions among spherical particles embedded in an elastic matrix. The interfaces between the particles and the matrix may or may not be perfect. The method is applied to the problem of determining the effective elastic moduli of composites when the interfaces satisfy a linear law. The effective properties are computed as functions of the volume fraction of the particles, the ratio of shear moduli, the Poisson ratios, and two parameters describing the linear interfacial characteristics of the inclusion-matrix interface. The results for the effective elastic properties for a wide range of these parameters are compared with effective-medium approximations and an agreement to within 30% is observed for the special case of hard-sphere random arrays considered in the study. We also consider a case of a three-phase composite material containing equal amounts of rigid inclusions and voids. The results for this case are compared with the predictions of a modified effective-medium approximation theory, and once again a similar level of agreement is found between the two.