The Edwards volume ensemble in cyclically sheared granular experiments

Abstract

We experimentally investigate the Edwards volume ensemble in cyclically sheared bidisperse disks of two friction coefficients (μ ≈ 0.3 and μ → ∞) subjected to a range of shear amplitudes γ_m. Despite the local and global anisotropy, hysteresis, and the potential long-range correlation of the free volume, the Edwards volume ensemble surprisingly provides an excellent statistical description of disk packings in cyclically sheared systems. Our finding can be better understood from the comprehensive analysis of the geometric and statistical properties of Voronoi cells of individual particles. First, the average degrees of anisotropy of Voronoi cells are weak at both the microscopic and macroscopic scales within a range of shear amplitudes γ_m of up to γ_m = 12% regardless of the inter-particle friction coefficients μ even though the azimuthal distributions of the Voronoi cell depend on μ. Second, there is only negligible hysteresis of global compactivity and volume fluctuations. Finally, the spatial correlations of the free volume and the orientation are weakly anisotropic and short ranged for practical purposes. Both results are independent of μ. Interestingly, our free-volume statistical results are consistent with the simple physical picture that the free volume is directly proportional to the compactivity.