A hyperbolic well-posed model for the flow of granular materials

A plasticity model for the flow of granular materials is presented which is derived from a physically based kinematic rule and which is closely related to the double-shearing model, the double-sliding free-rotating model and also to the plastic-potential model. All of these models incorporate various notions of the concept of rotation-rate and the crucial idea behind the model presented here is that it identifies this rotation-rate with a property associated with a Cosserat continuum, namely, the intrinsic spin. As a consequence of this identification, the stress tensor may become asymmetric. For simplicity, in the analysis presented here, the material parameters are assumed to be constant. The central results of the paper are that (a) the model is hyperbolic for two-dimensional steady-state flows in the inertial regime and (b) the model possesses a domain of linear well-posedness. Specifically, it is proved that incompressible flows are well-posed.