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 $ϕ_S \leq ϕ\leq ϕ_J$, for frictional granular disks, where above $ϕ_J$ 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 $ϕ$ system exhibits coupling between the shear strain, $γ$, and the pressure, $P$, which we characterize by the `Reynolds pressure', and a `Reynolds coefficient', $R(ϕ) = (\partial ^2 P/\partial γ^2)/2$. $R$ depends only on $ϕ$, and diverges as $R \sim (ϕ_c - ϕ)^α$, where $ϕ_c \simeq ϕ_J$, and $α\simeq -3.3$. Under cyclic shear, this system evolves logarithmically slowly towards limit cycle dynamics, which we characterize in terms of pressure relaxation at cycle $n$: $ΔP \simeq -β\ln(n/n_0)$. $β$ depends only on the shear cycle amplitude, suggesting an activated process where $β$ plays a temperature-like role.