Isostaticity in Cosserat continuum

Abstract

Under conditions of isostaticity in granular media, the contact forces for all particles are statically determinate and forces can be computed without recourse to deformation equations or constitutive relationships. Given that stresses represent spatial averages of inter-particle forces, the stress-equilibrium equations for the isostatic state form a hyperbolic system of partial differential equations that describe the internal stress state using only boundary tractions. In this paper, we consider a Cosserat medium and propose closure relationships in terms of stresses and couple stresses from observations of stress variations in the critical state regime from discrete element simulations an..