Critical Scaling of Shearing Rheology at the Jamming Transition of Soft Core Frictionless Disks

Abstract

We perform numerical simulations to determine the shear stress and pressure of steady-state shear flow in a soft-disk model in two dimensions at zero temperature in the vicinity of the jamming transition \phi_J. We use critical point scaling analyses to determine the critical behavior at jamming, and we find that it is crucial to include corrections to scaling for a reliable analysis. We find that the relative size of these corrections are much smaller for pressure than for shear stress. We furthermore find a superlinear behavior for pressure and shear stress above \phi_J, both from the scaling analysis and from a direct analysis of pressure data extrapolated to the limit of vanishing shear rate.