Reynolds Pressure and Relaxation in a Sheared Granular System

We describe experiments that probe the evolution of shear jammed states, occurring for packing fractions φS≤φ≤φJ, for frictional granular disks, where above φJ 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)=(∂²P/∂γ²)/2. R depends only on φ and diverges as R~(φc-φ)^α, where φcφJ and α-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-βln(n/n₀). β depends only on the shear cycle amplitude, suggesting an activated process where β plays a temperaturelike role.