Statistical mechanics description of an isotropic compression and its relationship to micromechanics

摘要

Statistical mechanics of volumes have been used to describe static packings of grains, usually grown by deposition or after shaking. In the present work, we use molecular dynamic simulations and the Gamma distribution of volumes introduced by Aste et. al [1, 2] to explore the limit equilibrium state of isotropic compression on a monodisperse system of spheres with sliding and rolling friction. The objective is to investigate how the volume entropy S, the compactivity χ and the number of elementary cells per particle C/N change with the microscopic force parameters among grains. First, we found that the volume distribution of the Voronoi tessellation on the final state actually follows the Gamma distribution proposed by Aste et. al. Next, we found that both S and χ grow smoothly by a factor of two with an increasing sliding friction coefficient μ_s, which, therefore, could be used as tunning parameter for these statistical variables. They also grow with the rolling friction coefficient μ_r, but for a smaller factor and reaching saturation very early. In contrast, C/N is almost unaffected by μ_r (between the error bars) and saturates for very small values of μ_(s,) but it can be reduced in around a 10% by decreasing the reduced elastic constant κ in two orders of magnitude, a change that does leave χ almost unaffected. These results drive the attention on μ_s as the most meaningful variable to control the reorganizations of grains through the isotropic compression and, thus, the statistical properties of its final state.