Shock Waves in Weakly Compressed Granular Media

TL;DR

This paper experimentally investigates nonlinear wave propagation in weakly compressed granular media, revealing a transition from sound waves to shock waves with pressure-dependent crossover and shock speed, characterized by powerlaw attenuation and energy balance.

Contribution

It provides experimental evidence for the pressure-dependent crossover from sound to shock waves and models shock attenuation with a logarithmic law, confirming recent theoretical predictions.

Findings

Crossover from sound to shock waves depends on confining pressure.

Shock wave speed is independent of confining pressure.

Shock attenuation follows a powerlaw with logarithmic dissipation law.

Abstract

We experimentally probe nonlinear wave propagation in weakly compressed granular media, and observe a crossover from quasi-linear sound waves at low impact, to shock waves at high impact. We show that this crossover grows with the confining pressure $P_0$, whereas the shock wave speed is independent of $P_0$ --- two hallmarks of granular shocks predicted recently. The shocks exhibit powerlaw attenuation, which we model with a logarithmic law implying that local dissipation is weak. We show that elastic and potential energy balance in the leading part of the shocks.