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

Jiang, M.J. and Harris, D. and Yu, H.S. (2005) Kinematic models for non-coaxial granular materials. Part I: theory. International Journal for Numerical and Analytical Methods in Geomechanics, 29 (7). pp. 643-661. ISSN 0363-9061 PDF Kinematic_Part_I.pdf Restricted to Repository staff only Download (416kB)

Abstract

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 © 2005 John Wiley & Sons, Ltd.

Item Type: Article non-coaxiality • plasticity • constitutive modelling • granular materials • micro-analysis • averaged micro-pure rotation rate MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systemsMSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solidsMSC 2010, the AMS's Mathematics Subject Classification > 86 Geophysics Ms Lucy van Russelt 12 Jul 2006 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/370 View Item