Micromechanical modeling of granular materials

We briefly review attempts to predict the mechanical response of granular materials based on a simple characterization of the interparticle force and the statistical geometry of their packing and interactions. The results of two such theories are presented. In the first, the particle displacements are assumed to be determined by the average strain. Here, features of the observed behavior are reproduced but the response of the aggregate is too stiff. In the second, a limited number of additional degrees of freedom are given to pairs of particles, the motion is constrained by force and moment equilibrium and the stiffness is reduced. Both approaches require a choice of state variables, whose values determine the incremental response and which, in turn, change their values with the deformation. Examples of state variables and their evolution are provided.