Local rheology of granular flows is controlled by granular temperature

We use discrete element simulations of granular flows to test a local rheological description of granular shear flows based on granular temperature. We test a variety of geometries, including (1) stress gradients, (2) spatial curvature, and (3) applied vibrations. Nonlocal granular fluidity models are known to capture stress gradients and spatial curvature, but applied vibrations cannot be captured directly by nonlocal fluidity models as formulated. We show that a single local rheology is sufficient to capture flows for all three cases above, including combinations. Temperature is generated both by shear and by applied vibrations and is then subject to a diffusion equation, which provides complete closure of the system and allows a fully local continuum description. We do observe some subtle differences, including anisotropy in the granular temperature tensor that depends on how temperature is generated. Our results suggest that a modified kinetic theory that directly treats temperature could be the way forward to describe arbitrary dense granular flows as well as a range of related soft material systems.