A numerical examination of shear banding and simple shear non-coaxial flow rules

Strain localisation and shear band formation is frequently observed during the handling and flow of dense phase particulate materials. However, a complete understanding of how shear bands form and what happens inside shear bands is still lacking. In order to address this problem, discrete particle simulations have been carried out to examine the detailed processes that occur at the grain scale associated with the initiation and development of shear bands. To reliably identify the continuum model applicable within a shear band is difficult due to the small number of particles/contacts involved. However, it is normally accepted that the mode of deformation within a shear band is one of simple shear. Consequently, simple shear simulations have been performed in order to determine the evolution of the stress tensor, dilation rate, and the principal directions of stress and strain-rate. It is demonstrated that the corresponding non-coaxial flow rule is equivalent to that suggested by Tatsuoka et al. (Geotechnique 38 148 (1988)). Furthermore, at fully developed flow when there is no further change in volume, the stress and strain-rate directions are coaxial and the flow rule is that proposed by Hill (The Mathematical Theory of Plasticity (Oxford University Press, 1950) p. 294).