Mean-field inelastic behavior of random arrays of identical spheres

We consider a random array of identical spheres that interact through noncentral contact forces. We assume that the displacement of a contact relative to a center may be calculated from the average strain of the aggregate. The normal component of the contact force is assumed to be Hertzian and the tangential component is assumed to be linearly elastic until frictional sliding occurs. We consider the response of the material in triaxial compression. For monotone deformations, we calculate the evolution of the contact distribution, the volume change, the stress-strain response, the plastic strain, and the strain hardening.