Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings

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 alpha, prepared at different global volume fractions phi(g). We find that Z is a monotonically increasing function of phi(g) for all alpha. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction phi(l) computed from a Voronoi tessellation. Z can be expressed as an integral over all values of phi(l): Z(phi(g), alpha, X) = integral Z(l)(phi(l), alpha, X)P(phi(l)/phi(g))d phi(l). The local contact number function Z(l)(phi(l), alpha, X) describes the relevant physics in term of locally defined variables only, including possible higher order terms X. The conditional probability P(phi(l)/phi(g)) to find a specific value of phi(l) given a global packing fraction phi(g) is found to be independent of a and X. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.