Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings

Abstract

In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α, prepared at different global volume fractions φg. We find that Z is a monotonically increasing function of φg for all α. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction φl computed from a Voronoi tessellation. Z can be expressed as an integral over all values of φl: Z(φg,α,X)=∫Zl(φl,α,X)P(φl|φg)dφl. The local contact number function Zl(φl,α,X) describes the relevant physics in term of locally defined variables only, including possible higher order terms X. The conditional probability P(φl|φg) to find a specific value of φl given a global packing fraction φg is found to be independent of α and X. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.