`Sinking' in a bed of grains activated by shearing

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, $c\propto ({\varphi }_c-\varphi {)}^a$, with $a\simeq 3$ and ${\varphi }_c\simeq {\varphi }_J$, reflecting the stiffening of granular systems under shear as $\varphi \to {\varphi }_J$. 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.

4 pages, 5 figures letter with supplementaries

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