(479g) A Non-Local Constitutive Model for Dense Granular Flows That Incorporates Shear-Induced Dilation

In the regime of dense slow flow, where grain interactions are abiding and Coulomb friction makes the dominant contribution to the shear stress, granular materials exhibit the phenomenon of shear-driven dilatancy that has no analogue in fluids. While considerable attention has been devoted in recent years to the kinematics, there is no satisfactory continuum description of dilatancy. We have shown recently that dilatancy can drive a large scale secondary flow that leaves a striking rheological signature. In recent years, several 'higher order' models have been proposed to regularize the kinematic indeterminacy of classical plasticity, but they all assume the granular medium to be incompressible. Here I present a non-local model that makes quasi-static flow kinematically determinate, and incorporates constant pressure dilation. The model is based on the simple idea that plastic deformation and density at any location are determined not just by the stress at that point, but in a mesoscopic region around it. This leads to a constitutive relation for the stress that involves the strain rate, density, and their Laplacian. The model differs in fundamental ways from the previously proposed non-local models, and does not require any additional variables to be introduced, such as the 'fluidity'. I will show that the predictions of the velocity and density fields in simple shear and in a substantially more complex flow compare favourably with observations in experiments and DEM simulations.