Shocks near Jamming

TL;DR

This paper demonstrates through simulations that near jamming, granular media exhibit supersonic shocks instead of phonons, with shock properties well-described by a simple analytical model.

Contribution

It reveals that elementary excitations near jamming are non-linear shocks and provides an analytical model for shock speed dependence on pressure and impact.

Findings

Granular media near jamming support supersonic shocks.

Shock speed depends on pressure and impact intensity.

A simple analytical model accurately describes shock behavior.

Abstract

Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed, and demonstrate that the elementary excitations are strongly non-linear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.