Geometry of frictionless and frictional sphere packings

Silbert, Leonardo E.; Ertaş, Deniz; Grest, Gary S.; Halsey, Thomas C.; Levine, Dov

doi:10.1103/physreve.65.031304

Cited by 362 publications

(478 citation statements)

References 15 publications

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“…g z (r) measures the number of balls with their volume intersecting the surface of a sphere of radius r measured from the center of a given ball. When r = R in (30) we obtain the mechanical coordination number while the geometrical one is obtained for a small value ∆r = r−R 2R = 0 for which we distinctly find a signature from computer simulations, unambiguously defining it at ∆r = 0.04. Furthermore, as shown in the figures, we find that g z (∆r) along the RCP line, increases slightly as ∆r increases, and finally reach the same value of g z at ∆r = 0.04 as shown in Fig.…”

Section: Geometrical Versus Mechanical Coordination Number: Measuringmentioning

confidence: 63%

“…Previous results find power law scaling [29,30,27,32] where the stress vanishes as σ ∼ (φ − φ c ) α . A possible scenario is depicted in the extended phase diagram of Fig.…”

Section: Discussionmentioning

confidence: 92%

“…(b) Critical phenomena of deformable particle: jamming is seen as a critical point at which observables such as pressure, coordination number and elastic moduli behave as power-law near the critical volume fraction, φ c , [26,27,29,31,32,30,28,33,34]. The jammed state is modelled as granular media composed of soft particles, typically Hertz-Mindlin [32,35,36] grains under external pressure and emulsions compressed under osmotic pressure [37], as they approach the jamming transition from the solid phase above the critical density: φ → φ + c .…”

Section: Understanding Jammingmentioning

confidence: 99%

“…In practice, it is widely believed that the isostatic condition is necessary for a jammed disordered packing following the Alexander conjecture [59,60,61] which was tested in several works [27,29,30,33] It is well known that mechanical equilibrium imposes an average coordination number larger or equal than a minimum coordination where the number of force variables equals the number of force and torque balance equations [59,61,60]. The so-called isostatic condition.…”

Section: Definition Of Jamming: Isostatic Conjecturementioning

confidence: 99%

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Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

Wang

Jin

et al. 2011

Physica A: Statistical Mechanics and its Applications

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The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications spanning from the mathematician's pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ∼ 55% (named random loose packing, RLP) while filling all the loose voids results in a maximum density of ∼ 63 − 64% (named random close packing, RCP). While those values seem robustly true, to this date there is no well-accepted physical explanation or theoretical prediction for them. Here we develop a common framework for understanding the random packings of monodisperse hard spheres whose limits can be interpreted as the experimentally observed RLP and RCP. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volumes of the constituent grains (denoted the volume function) and the number of neighbors in contact that permits to simple combine the two approaches to develop a theory of volume fluctuations in jammed * Corresponding author

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Section: Geometrical Versus Mechanical Coordination Number: Measuringmentioning

confidence: 63%

“…Previous results find power law scaling [29,30,27,32] where the stress vanishes as σ ∼ (φ − φ c ) α . A possible scenario is depicted in the extended phase diagram of Fig.…”

Section: Discussionmentioning

confidence: 92%

Section: Understanding Jammingmentioning

confidence: 99%

Section: Definition Of Jamming: Isostatic Conjecturementioning

confidence: 99%

See 2 more Smart Citations

Jamming II: Edwards’ statistical mechanics of random packings of hard spheres

Wang

Jin

et al. 2011

Physica A: Statistical Mechanics and its Applications

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“…When compacting loose granular material, density and connectivity increase until a static state is reached, where the material withstands the external pressure. Such jammed states are currently widely studied [1,2,3].…”

Section: Introductionmentioning

confidence: 99%

The effect of contact torques on porosity of cohesive powders

et al. 2005

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The porosity of uniaxially compacted cohesive powders depends on the applied stress (including gravity). The case, where these stresses are weak, is considered. The compaction results in a porosity which is a function of sliding, rolling and torsion friction. By contact dynamics simulations it is shown that the influences of contact torques (static rolling and torsion friction) on the porosity are significant and approximately additive. The relevance for nano-powder pressure sintering is discussed.

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