Plane deformations of ideal granular materials3

The flow rule based on a double-shearing model developed by A. J. M. Spencer, and M. M. Mehrabadi and S. C. Cowin is intended for use in analyzing fully developed plane flows of rate-independent, isotropic, rigidperfectly plastic frictional and dilatant granular materials. With the view of extending the range of applicability of this physically based flow rule to the prepeak (prelocalization) regime, we systematically introduce isotropic hardening (softening) via the usual consideration of scalar hardening variables in the yield function. However, for this new model to be in accord with some recent experimental observations of I. Vardoulakis on shear-band localizations, it is found that we have to abandon the classical assumption of the coincidence of stress and velocity characteristics.