Reynolds Pressure and Relaxation in a Sheared Granular System

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’, $R(\phi) = (\partial ^2 P/\partial \gamma ^2)/2$\mathrm{.}$R$dependsonlyon$\phi$,anddivergesas$R \sim (\phi_c - \phi)^{\alpha}$,where$\phi_c \simeq \phi_J$,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 $n$: $\mathrm{\Delta }P\simeq -\beta \ln (n\mathrm{/}{n}_0)$. $\beta$ depends only on the shear cycle amplitude, suggesting an activated process where $\beta$ plays a temperature-like role.