Local Rheology of Dense Granular Flows with Temperature Generation from Vibration and Pressure Gradients.

We use discrete element simulations of granular flows that include both stress gradients as well as applied vibrations to seek a universal constitutive law that includes local granular temperature. Nonlocal granular fluidity models are known to capture systems with stress gradients, and recent work has shown that these models are also consistent with a local rheology based on granular temperature, defined as the mean-square of grain velocity fluctuations. Applied vibrations cannot be captured directly by nonlocal fluidity models as formulated, since granular temperature is not treated directly. We find that a single local rheology is sufficient to capture flows including either vibrations or stress gradients, as well as both simultaneously. 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 also observe that reduction in material friction due to granular temperature is associated with reduction in the anisotropy of contacts and forces, providing a grain-scale picture for how friction is reduced. Additionally We show that a diffusion equation is sufficient to capture our results in certain limits, which would close the system of equations. 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.