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 ${\varphi }_g$. We find that $Z$ is a monotonously increasing function of ${\varphi }_g$ 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 ${\varphi }_l$ computed from a Voronoi tessellation. $Z$ can be expressed as an integral over all values of ${\varphi }_l$: $Z({\varphi }_g,\alpha ,X)=\int Z_l({\varphi }_l,\alpha ,X)P({\varphi }_l|{\varphi }_g)d{\varphi }_l$. The local contact number function $Z_l({\varphi }_l,\alpha ,X)$ describes the relevant physics in term of locally defined variables only, including possible higher order terms $X$. The conditional probability $P({\varphi }_l|{\varphi }_g)$ to find a specific value of ${\varphi }_l$ given a global packing fraction ${\varphi }_g$ 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.

more revisions, accepted for publication in Physical Review Letters

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• Cuddling Ellipsoids: Densest local structures of uniaxial ellipsoids
• Mixing properties of bi-disperse ellipsoid assemblies: Mean-field behaviour in a granular matter experiment
• Local analysis of the history dependence in tetrahedra packings