Velocity Profiles in Repulsive Athermal Systems under Shear

TL;DR

This study uses molecular dynamics simulations to explore how athermal systems under shear develop nonlinear velocity profiles and boundary-dependent behaviors, revealing critical shear velocities and the influence of damping and packing density.

Contribution

It introduces a detailed analysis of velocity profiles in sheared athermal systems, highlighting the role of damping, packing fraction, and shear wave speed in determining flow behavior.

Findings

Nonlinear velocity profiles occur above a critical shear velocity $u_c$.

Dilation and velocity fluctuations increase near the moving boundary.

Underdamped systems have $u_c$ linked to shear wave speed and approach zero near $ ho_c$.

Abstract

We conduct molecular dynamics simulations of athermal systems undergoing boundary-driven planar shear flow in two and three spatial dimensions. We find that these systems possess nonlinear mean velocity profiles when the velocity $u$ of the shearing wall exceeds a critical value $u_c$. Above $u_c$, we also show that the packing fraction and mean-square velocity profiles become spatially-dependent with dilation and enhanced velocity fluctuations near the moving boundary. In systems with overdamped dynamics, $u_c$ is only weakly dependent on packing fraction $\phi$. However, in systems with underdamped dynamics, $u_c$ is set by the speed of shear waves in the material and tends to zero as $\phi$ approaches $\phi_c$. In the small damping limit, $\phi_c$ approaches values for random close-packing obtained in systems at zero temperature. For underdamped systems with $\phi<\phi_c$, $u_c$ is zero and thus they possess nonlinear velocity profiles at any nonzero boundary velocity.