Compliance of Assemblage of Unlike Elastic Spheres

An investigation is made of the load-response behavior of a simple granular cell consisting of the following: two like elastic spheres separated at zero load by a ring of restrained smaller elastic spheres arranged about a loading axis passing through the centers of the primary spheres. The load-response relations may be elastic or inelastic depending on the radii ratio, elastic properties, and magnitude of radial restraint imposed on the smaller spheres. The compliance of the assemblage is found to be of the same order as for two large spheres only in contact. For small radii ratios, the response is inelastic, and the energy dissipated in friction between the surfaces of the unlike spheres is significant.