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The structure of random ellipsoid packings


Schaller,  Fabian M.
Group Statistical mechanics of granular media, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Schaller, F. M. (2012). The structure of random ellipsoid packings. Diploma Thesis, Friedrich-Alexander Universität, Erlangen-Nürnberg.

Disordered packings of ellipsoidal particles are an important model for disordered granular matter and can shed light on geometric features and structural transitions in granular matter. In this thesis, the structure of experimental ellipsoid packings is analyzed in terms of contact numbers and measures from mathematical morphometry to characterize of Voronoi cell shapes. Jammed ellipsoid packings are prepared by vertical shaking of loose configurations in a cylindrical container. For approximately 50 realizations with packing fractions between 0.54 and 0.70 and aspect ratios from 0.40 to 0.97, tomographic images are recorded, from which positions and orientations of the ellipsoids are reconstructed. Contact numbers as well as discrete approximations of generalized Voronoi diagrams are extracted. The shape of the Voronoi cells is quantified by isotropy indexes b,r,s,n based on Minkowski tensors. In terms of the Voronoi cells, the behavior for jammed ellipsoids differs from that of spheres; the Voronoi Cells of spheres become isotropic with increasing packing fraction, whereas the shape of the Voronoi Cells of ellipsoids with high aspect ratio remains approximately constant. Contact numbers are discussed in the context of the jamming paradigm and it is found that the frictional ellipsoid packings are hyperstatic, i.e. have more contacts than are required for mechanical stability. It is observed, that the contact numbers of jammed ellipsoid packings predominantly depend on the packing fraction, but also a weaker dependence on the aspect ratio and the friction coefficient is found. The achieved packing fractions in the experiments lie within upper and lower limits expected from DEM simulations of jammed ellipsoid packings. Finally, the results are compared to Monte Carlo and Molecular Dynamics data of unjammed equilibrium ellipsoid ensembles. The Voronoi cell shapes of equilibrium ensembles of ellipsoidal particles with a low aspect ratio become more anisotropic by increasing the packing fraction, while the cell shape of particles with large aspect ratios does the opposite. The experimental jammed packings are always more anisotropic than the corresponding densest equilibrium configuration.