On the relationship between stress–dilatancy, anisotropy, and plastic dissipation for granular materials

Techniques of modern thermomechanics are used to analyse the stress–dilatancy relation for shear deformations of frictional, granular materials. Central to this approach is the recognition that in general, deformations of granular materials can involve stored plastic work. It is recognised that in shear deformations, where the shape of the grains induces the dilatancy, the confining pressure is a constraint and dissipates no energy. Nevertheless it is shown that, in such a shear deformation, the total plastic work rate is equal to the rate of energy dissipation, and that this is given by Thurairajah's classical observations. It is further shown that anisotropy is necessarily induced, and that the stress–dilatancy relation is given by Taylor's well-known formula. It is also demonstrated that the extant procedure for deducing yield conditions and flow rules from specified dissipation functions is invalid.