Reynolds Pressure and Relaxation in a Sheared Granular System

Jie Ren, Joshua A. Dijksman, Robert P. Behringer
2013 Physical Review Letters  
We describe experiments that probe the evolution of shear jammed states, occurring for packing fractions ϕ_S ≤ϕ≤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) = (∂ ^2 P/∂γ ^2)/2. R
more » ... ends only on ϕ, and diverges as R ∼ (ϕ_c - ϕ)^α, where ϕ_c ≃ϕ_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: Δ P ≃ -β(n/n_0). β depends only on the shear cycle amplitude, suggesting an activated process where β plays a temperature-like role.
doi:10.1103/physrevlett.110.018302 pmid:23383846 fatcat:nfbeqg2gnvcina4zyzxovp32fi