A simplified model for inelastic behavior of an idealized granular material

In this paper, our main interest is to describe the inelastic behavior of a granular material in the range of deformation that precedes localization. We do this in the simplest possible way, by idealizing the material as a random array of identical, elastic, frictional spheres and assuming that particles move with the average strain. The contact force is assumed non-central: the normal component follows the Hertz’s law, while the tangential component is elastic until frictional-sliding occurs. We provide an analytical description of this material in triaxial extension and compression at fixed pressure, for both loading and unloading. We obtain expressions for the stress–strain relation, the plastic strain, the elastic and plastic volume change, the strain hardening and the potential function. We assume the Mohr–Coulomb criterion for yielding and we obtain an explicit expression between dilatancy and stress in the material.