Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

TL;DR

This study uses molecular dynamics simulations to explore how dense granular systems under shear develop velocity profiles, revealing conditions for linearization, instability, and shear band formation related to granular temperature and shear stress.

Contribution

It demonstrates the long-term instability of nonlinear velocity profiles and identifies conditions for their stability and shear band formation in sheared granular systems.

Findings

Nonlinear velocity profiles are unstable at long times.

Linear velocity profiles form when temperature and density are uniform.

Shear bands form when shear stress is below yield stress.

Abstract

We perform molecular dynamics simulations of model granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time $t_l$ required for the velocity profiles to become linear and find that $t_l$ increases as a power-law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.