The velocity equations for dilatant granular flow and a new exact solution

Abstract.

For axially symmetric flow of dilatant granular materials, the velocity equations uncouple from the stress equations in certain plastic regimes, and assuming dilatant double shearing a set of three first order partial differential equations are obtained. These equations turn out to be deceptive because although simple in appearance, the determination of simple exact solutions is non-trivial. Here we show that all the known functional forms of existing solutions also arise systematically by consideration of the "optimal systems" of the classical Lie symmetries which indicates that any further solution types most likely arise from non-classical symmetries. For one of the known families we present a special case which admits a particularly simple closed form expression, which has not been previously given in the literature. For this particular special case the integral curves (streamlines) can be readily obtained as well as a simple analytical "approximation" for the particle paths. The streamlines and the validity of the analytical approximation are shown graphically.