Uniform Shock Waves in Disordered Granular Matter

TL;DR

This paper investigates how energy transport in granular matter shifts from phonons to nonlinear shocks as confining pressure decreases, revealing a transition to nonlinear wave behavior near the jamming point.

Contribution

It introduces a combined simulation and theoretical framework to analyze shock wave propagation in granular media at low pressures, highlighting the nonlinear energy transport regime.

Findings

Shock waves dominate energy transport at low pressures.

Shock speed depends on pressure and impact intensity.

Nonlinear waves become increasingly important near jamming.

Abstract

The confining pressure $P$ is perhaps the most important parameter controlling the properties of granular matter. Strongly compressed granular media are, in many respects, simple solids in which elastic perturbations travel as ordinary phonons. However, the speed of sound in granular aggregates continuously decreases as the confining pressure decreases, completely vanishing at the jamming-unjamming transition. This anomalous behavior suggests that the transport of energy at low pressures should not be dominated by phonons. In this work we use simulations and theory to show how the response of granular systems becomes increasingly nonlinear as pressure decreases. In the low pressure regime the elastic energy is found to be mainly transported through nonlinear waves and shocks. We numerically characterize the propagation speed, shape, and stability of these shocks, and model the dependence of the shock speed on pressure and impact intensity by a simple analytical approach.