`Sinking' in a bed of grains activated by shearing

TL;DR

This study demonstrates how a weak force enables intruder movement in dense granular materials under shear, revealing a linear relationship with shear amplitude and force, and showing that motion vanishes near jamming density.

Contribution

It introduces a novel mechanism where small forces cause intruder motion during fragile states in sheared granular media, highlighting the role of shear reversals and jamming.

Findings

Intruder motion occurs during fragile states generated by shear reversals.

Net intruder displacement per cycle is proportional to shear amplitude and force.

Motion vanishes as density approaches jamming point, following a power law.

Abstract

We show how a weak force, $f$, enables intruder motion through dense granular materials subject to external mechanical excitations, in the present case stepwise shearing. A force acts on a Teflon disc in a two dimensional system of photoelastic discs. This force is much smaller than the smallest force needed to move the disc without any external excitation. In a cycle, material + intruder are sheared quasi-statically from $\gamma = 0$ to $\gamma_{max}$, and then backwards to $\gamma = 0$. During various cycle phases, fragile and jammed states form. Net intruder motion, $\delta$, occurs during fragile periods generated by shear reversals. $\delta$ per cycle, e.g. the quasistatic rate $c$, is constant, linearly dependent on $\gamma_{max}$ and $f$. It vanishes as, $c \propto (\phi_c - \phi)^a$, with $a \simeq 3$ and $\phi_c \simeq \phi_J$, reflecting the stiffening of granular systems under shear as $\phi \rightarrow \phi_J$. The intruder motion induces large scale grain circulation. In the intruder frame, this motion is a granular analogue to fluid flow past a cylinder, where $f$ is the drag force exerted by the flow.