Improving the Density of Jammed Disordered Packings Using Ellipsoids

Department of Mathematics, Cornell University, Итак, New York, United States
Science (Impact Factor: 33.61). 02/2004; 303(5660):990-3. DOI: 10.1126/science.1093010
Source: PubMed


Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics
and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible
packing fraction . It is also well known that certain random (amorphous) jammed packings have φ ≈ 0.64. Here, we show experimentally and with
a new simulation algorithm that ellipsoids can randomly pack more densely—up to φ= 0.68 to 0.71for spheroids with an aspect
ratio close to that of M&M's Candies—and even approach φ ≈ 0.74 for ellipsoids with other aspect ratios. We suggest that the
higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle
contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z ≈ 10 for our spheroids, as compared to Z ≈ 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular
media and ceramics, glass formation, and discrete geometry.

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    • "Nous avons opté pour des systèmes discrets polydisperses lesquels sont moins sujets aux effets d'anisotropie. La fraction surfacique occupée par les cylindres est proche de 87% avec un nombre de coordination proche de 4,5 ce qui correspond à un random close packing en 2D [3]. Afin d'assurer l'isotropie du système, le nombre de particules a été fixé à 15000 après étude de la distribution des angles de contact. "
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    ABSTRACT: La méthode des éléments discrets s’avère une approche adaptée pour la simulation du comportement mécanique de milieux continus homogènes pour lesquels des phénomènes locaux tels que l’endommagement et la fissuration interviennent. Dans cette communication, nous nous intéressons aux milieux continus hétérogènes pour lequel un travail important de validation reste encore à réaliser. Nous nous limitons au domaine de l’élasticité linéaire en 2D et considérons le cadre des éléments discrets cohésifs qui couple le modèle particulaire à un modèle lattice de type poutre. Des tests de validation sont réalisés et des comparaisons effectuées avec des méthodes classiques d’homogénéisation pour différentes configurations et contrastes de propriétés
    Full-text · Conference Paper · May 2015
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    • "/ m depends on the distribution of particle sizes and shapes, as well as the packing geometry [e.g., McGeary, 1961; Milewski, 1973; Ouchiyama and Tanaka, 1981; Wildemuth and Williams, 1984; Sudduth, 1993; Yu et al., 1996; Torquato et al., 2000; Zou et al., 2003; Donev et al., 2004; Weitz, 2004; Bournonville et al., 2005; Brouwers, 2006; Prior et al., 2013; Baule and Makse, 2014]. For example, for spheres in cubic or in random close packing, / m % 0:52 or 0.74, respectively; and for random close packing of ellipsoids, / m % 0:74 (for aspect ratio % 1.3) [Donev et al., 2004]. Here we are interested in the random close packing of mixtures of particles of different shapes and sizes, seeking a functional relationship of / m by measuring / m experimentally for a range of modalities in particle size and shape. "

    Full-text · Article · Jan 2015 · Geochemistry Geophysics Geosystems
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    • "For example, for the largest system examined herein, the maximal value of ⟨C⟩ (at α = 2.5) is 6.8. This value is less than ⟨C⟩ = 9.82, which is found in jammed packings of elongated ellipsoids [8] and reflects the higher porosity of the packings presented herein. The origin of the minima at α = 1.05 is not clear. "
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    ABSTRACT: We use numerical simulations based on the discrete element method (DEM) to study the response of a cuboidal assembly of spherical (diameter dd) or spheroidal particles to uniaxial compression. This study examines the influences of slight deviations from the spherical shape of particles or of the thickness of cuboidal samples on the packing and mechanical characteristics of the assembly. The spheroidal particles were fabricated by the multisphere method. Eight different particle shapes were considered, each with the same volume and with aspect ratios αα from 1.01.0 to 2.52.5. The final vertical height and larger horizontal depth of the cuboidal deposit were 15d15d, whereas the thickness ranged from 1.025d1.025d to 10d10d. Upon increasing the assembly thickness or deviating from a spherical shape, numerical examinations by the DEM revealed clear differences in the packing structure and uniaxial compression of assemblies of spheroidal particles. The departure from a spherical shape results in intense changes in contact network, which is manifested as changes in the volume fraction, mean number of contacts per particle, and ordering of the deposits. For the more elongated particles, the pressure ratio as a function of spheroid aspect ratio reached nearly constant values regardless of the sample thickness.
    Full-text · Article · Dec 2014 · Physica A: Statistical Mechanics and its Applications
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