Reynolds Pressure and Relaxation in a Sheared Granular System

Abstract

We describe experiments that probe the evolution of shear jammed states, occurring for packing fractions ${\varphi }_S\le \varphi \le {\varphi }_J$, for frictional granular disks, where above ${\varphi }_J$ there are no stress-free static states. We use a novel shear apparatus that avoids the formation of inhomogeneities known as shear bands. This fixed $\varphi$ system exhibits coupling between the shear strain, $\gamma$, and the pressure, $P$, which we characterize by the `Reynolds pressure', and a `Reynolds coefficient', $R(\varphi )=({\partial }^{2}P/\partial {\gamma }^2)/2$. $R$ depends only on $\varphi$, and diverges as $R\sim ({\varphi }_c-\varphi {)}^{\alpha }$, where ${\varphi }_c\simeq {\varphi }_J$, and $\alpha \simeq -3.3$. Under cyclic shear, this system evolves logarithmically slowly towards limit cycle dynamics, which we characterize in terms of pressure relaxation at cycle $n$: $\Delta P\simeq -\beta \ln (n/n_0)$. $\beta$ depends only on the shear cycle amplitude, suggesting an activated process where $\beta$ plays a temperature-like role.

4 pages, 4 figures