A micromechanically-based constitutive model for frictional deformation of granular materials

Abstract

A micromechanically-based constitutive model is developed for inelastic deformation of frictional granular assemblies. It is assumed that the deformation is produced by relative sliding and rolling of granules, accounting for pressure sensitivity, friction, dilatancy (densification), and, most importantly, the fabric (anisotropy) and its evolution in the course of deformation. Attention is focused on two-dimensional rate-independent cases. The presented theory fully integrates the micromechanics of frictional granular assemblies at the micro- (grains), meso- (large collections of grains associated with sliding planes), and macro- (continuum) scales. The basic hypothesis is that the deformation of frictional granular masses occurs through simple shearing accompanied by dilatation or densification (meso-scale), depending on the microstructure (micro-scale) and the loading conditions (continuum-scale). The microstructure and its evolution are defined in terms of the fabric and its evolution. While the elastic deformation of most frictional granular assemblies is rather small relative to their inelastic deformation, it is included in the theory, since it affects the overall stresses.