On the problem of linear elasticity for an infinite region containing a finite number of non-intersecting spherical inhomogeneities

Abstract The problem of linear elasticity for an infinite number of non-intersecting spherical and, more generally, ellipsoidal inhomogeneities is attacked. The approach taken does not misrepresent geometry of inhomogeneities, although the continuity conditions at the intefaces are only approximately satisfied. The principal idea of the approach is to extend the method of Kachanov (1985, Int. J. Fracture28, R11–R19; 1987, Int. J. Solids Structures23, 23–43) for interacting cracks to the realm of the Eshelby equivalent inclusion method. The application to a test problem for two spherical cavities suggests that the approach can be useful for predictions of the overall response of composite materials and interfacial stress concentrations.