`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 $γ= 0$ to $γ_{max}$, and then backwards to $γ= 0$. During various cycle phases, fragile and jammed states form. Net intruder motion, $δ$, occurs during fragile periods generated by shear reversals. $δ$ per cycle, e.g. the quasistatic rate $c$, is constant, linearly dependent on $γ_{max}$ and $f$. It vanishes as, $c \propto (ϕ_c - ϕ)^a$, with $a \simeq 3$ and $ϕ_c \simeq ϕ_J$, reflecting the stiffening of granular systems under shear as $ϕ\rightarrow ϕ_J$. 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.