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 $\alpha$, prepared at different global volume fractions $\phi_g$. We find that $Z$ is a monotonously 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 $\phi_l$: $Z(\phi_g, \alpha, X) = \int Z_l (\phi_l, \alpha, X) \; P(\phi_l | \phi_g) \; d\phi_l$. 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 $\alpha$ and $X$. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.