Reynolds pressure and relaxation in a sheared granular system

We describe experiments that probe the evolution of shear jammed states, occurring for packing fractions [symbol: see text](S) ≤ [symbol: see text] ≤ [symbol: see text] J, for frictional granular disks, where above [symbol: see text]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 [symbol: see text] system exhibits coupling between the shear strain, γ, and the pressure, P, which we characterize by the "Reynolds pressure" and a "Reynolds coefficient," R([symbol: see text]) = (∂(2)P/∂γ(2))/2. R depends only on [symbol: see text] and diverges as R ~ ([symbol: see text])c - )(α), where [symbol: see text](c) ~/= [symbol: see text](J) 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/n(0)). β depends only on the shear cycle amplitude, suggesting an activated process where β plays a temperaturelike role.