Some Properties of a New Model for Slow Flow of Granular Materials

Abstract

Some properties of a new continuum model for the bulk flow of a dense granular material in which neighbouring grains are in contact for a finite duration of time and in which the contact force is non-impulsive – the so called slow flow regime – are presented. The model generalises both the plastic potential and double-shearing models and contains an additional kinematic quantity – the intrinsic spin. The stress tensor is, in general, non-symmetric and separate yield conditions govern translational and rotational yield. We consider homogeneous, quasi-static loadings for the symmetric part of the stress and dynamic loading for the anti-symmetric part of the stress. A solution for the stress state in terms of a single parameter, namely the major principal direction of the symmetric part of the stress, is presented. This direction itself is determined by a consideration of the flow equations in the context both dilatant and isochoric simple shear flows. These simple flows are used to complete the characterisation of the relationship between the anti-symmetric part of the stress and the intrinsic spin.