Improving the density of jammed disordered packings using ellipsoids

Department of Mathematics, Cornell University, Итак, New York, United States
Science (Impact Factor: 31.48). 02/2004; 303(5660):990-3. DOI: 10.1126/science.1093010
Source: PubMed

ABSTRACT 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.

Download full-text


Available from: R. Connelly, Feb 15, 2015
  • Source
    Geochemistry Geophysics Geosystems 01/2015; · 3.05 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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.
    Physica A: Statistical Mechanics and its Applications 12/2014; 416:279–289. DOI:10.1016/j.physa.2014.08.063 · 1.72 Impact Factor
  • Source