Non-universal Voronoi cell shapes in amorphous ellipsoid packings

Abstract

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoi diagram of configurations of oblate ellipsoids, for various aspect ratios \(\alpha\) and global volume fractions \(\phi_g\). We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction \(\phi_l\), defined as the particle's volume divided by its Voronoi cell volume. We find that the probability \(P(\phi_l)\) for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of \(\phi_g\) as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index \(\beta=\beta_0^{2,0}\), points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape \(\beta\) of all cells with a given value of \(\phi_l\) is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.