Kinematic models for non-coaxial granular materials. Part I: theory

The purpose of this paper is to present a physically based plasticity model for non-coaxial granular materials. The model, which we shall call the double slip and rotation rate model (DSR2 model), is a pair of kinematic equations governing the velocity field. The model is based on a discrete micro-analysis of the kinematics of particles in contact, and is formulated by introducing a quantity called the averaged micro-pure rotation rate (APR) into the unified plasticity model which was proposed by one of the authors. Our macro-micro mechanical analysis shows that the APR is a non-linear function of, among other quantities, the macro-rotation rate of the major principal axis of stress taken in the opposite sense. The requirement of energy dissipation used in the double-sliding free-rotating model appears to be unduly restrictive as a constitutive assumption in continuum models. In the DSR2 model the APR tensor and the spin tensor are directly linked with non-coaxiality of the stress and deformation rate tensors. We also propose a simplified plasticity model based on the DSR2 model for a class of dilatant materials, and analyse its material stability. Copyright (c) 2005 John Wiley & Sons, Ltd.