An equilibrium-based approach for the micromechanical modelling of a non-linear elastic granular material

A micromechanical model is developed to describe the non-linear elastic behavior of an isotropic granular solid consisting of a random package of identical elastic spheres. The contact points are assumed to be equally distributed in all directions and contact points on a same particle are represented by random variables which are correlated in order to consider the effect of impenetrability of the spheres on the contact points distribution. A new equilibrium-based approach is adopted: for a given macroscopic stress, a system of consistent contact forces satisfying the equilibrium of each particle is determined and the relative displacements between particles are obtained from the contact forces by using the non linear contact law of the Hertz-Cattaneo-Mindlin theory. The macroscopic strain tensor compatible with the relative displacements above is determined by means of the virtual force theorem. Analytical solutions are derived, which results that display good agreement with the experimental observations for random packages of glass microspheres as well as with the empirical predictions provided by the Hardin law for sand and gravel.