The effects of particle dynamics on the calculation of bulk stress in granular media

Expressions for bulk stress within a granular material in a dynamic setting are reviewed and explicitly derived for assemblies of three dimensional arbitrary shaped particles. By employing classical continuum and rigid body mechanics, the mean stress tensor for a single particle is separated into three distinct components; the familiar Love–Webber formula describing the direct effect of contacts, a component due to the net unbalanced moment arising from contact and a symmetric term due to the centripetal acceleration of material within the particle. A case is made that the latter term be ignored without exception when determining bulk stress within an assembly of particles. In the absence of this centripetal term an important observation is made regarding the nature of the symmetry in the stress tensor for certain types of particles; in the case of particles with cubic symmetry, the effects of dynamics on the bulk stress in an assembly is captured by an entirely skew-symmetric tensor. In this situation, it is recognised that the symmetric part of the Love–Webber formula is all that is required for defining the mean stress tensor within an assembly – regardless of the dynamics of the system.