Micromechanical Formulation of Stress Dilatancy as a Flow Rule in Plasticity of Granular Materials

Abstract

The paper presents micromechanical formulations of stress dilatancy and their connection to a flow rule in classical elastoplasticity. Dilatancy is inarguably the manifestation of an internal kinematic constraint involving both particle shape and connectivity (texture or fabric) with operative interparticle friction against applied stresses. However, this notion of microstructural dependence is nonexistent in most stress-dilatancy formulations in the literature. We present two different micromechanical approaches that arrive at stress-dilatancy expressions with embedded micromechanical information in the form of a second-order fabric tensor. In connection to stress dilatancy, the underlying nature of the flow rule is next discussed with respect to the dependence of the plastic strain increment vector on the direction of loading (stress increment). It is demonstrated analytically that the flow rule is singular in three-dimensional stress and strain conditions. Finally, the dependencies of dilatancy on fabric are illustrated through various numerical simulations using the micromechanically enriched stress-dilatancy models and a discrete element method.