  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.
