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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 $α$, prepared at different global volume fractions $ϕ_g$. We find that $Z$ is a monotonously increasing function of $ϕ_g$ 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 $ϕ_l$ computed from a Voronoi tessellation. $Z$ can be expressed as an integral over all values of $ϕ_l$: $Z(ϕ_g, α, X) = \int Z_l (ϕ_l, α, X) \; P(ϕ_l | ϕ_g) \; dϕ_l$. The local contact number function $ Z_l (ϕ_l, α, X)$ describes the relevant physics in term of locally defined variables only, including possible higher order terms $X$. The conditional probability $P(ϕ_l | ϕ_g)$ to find a specific value of $ϕ_l$ given a global packing fraction $ϕ_g$ 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.