Effect of Collisional Elasticity on the Bagnold Rheology of Sheared Frictionless Two Dimensional Disks

Abstract: We carry out constant volume simulations of steady-state, shear driven flow in a simple model of athermal, bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. Focusing on the small strain rate limit, we map out the rheological behavior as a function of particle packing fraction $\phi$ and a parameter $Q$ that measures the elasticity of binary particle collisions. We find a $Q^*(\phi)$ that marks the clear crossover from a region characteristic of strongly inelastic collisions, $Q<Q^*$, to a region characteristic of weakly inelastic collisions, $Q>Q^*$, and give evidence that $Q^*(\phi)$ diverges as $\phi\to\phi_J$, the shear driven jamming transition. We thus conclude that the jamming transition at any value of $Q$ behaves the same as the strongly inelastic case, provide one is sufficiently close to $\phi_J$. We further characterize the differing nature of collisions in the strongly inelastic vs weakly inelastic regions, and recast our results into the constituent equation form commonly used in discussions of hard granular matter.