Non-Affine Dynamics and Local Shear Rate in a Sheared Granular System*

Granular media are large collections of disordered macroscopic particles interacting via dissipative forces. We focus on the effect of fixed pins on the dynamics of an athermal sheared system in two dimensions. The system consists of a binary 50:50 mixture of radii 1.0:1.4 and additional fixed pins of radius 0.004. A shear is applied by moving the top and bottom walls, made of frozen particles. We study the non-affine dynamics by determining the D2min profile. Despite vertical symmetry in our shearing geometry, when pins are absent the long-lasting fluctuations in stress yield an asymmetric D2min profile. This occurs even when the system is sheared over an extremely large range (a dimensionless strain of around 1.) However, as pin density increases, the D2min profile is increasingly symmetric, with higher D2min values found closer to the walls. Via the velocity profile we determine the local shear rate, and find qualitatively the same profile shapes for D2min and the local shear rate.