A non-local constitutive model for slow granular flow that incorporates dilatancy

Over the past two decades several attempts have been made to formulate constitutive models for slow granular flow to remedy the deficiencies of classical plasticity. All the proposed models assume the medium to be incompressible, though it is well known that density change accompanies deformation in granular materials. A particularly important aspect of density change that is distinctive of granular materials is dilatancy, or volume deformation caused by shear deformation. No constitutive model for sustained flow has thus far captured dilatancy. Here we present a non-local constitutive model wherein the deformation rate and density at a point depend on the state of stress in a mesoscopic region around it. Apart from incorporating dilatancy, our model has a physical origin that is distinct from that of the previously proposed non-local models. We test our model on simple shear flow in the absence and presence of gravity, and find its predictions to be in good agreement with particle dynamics simulations.