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arXiv · 1104.4933

Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids

Kyle C. Smith·Meheboob Alam·Timothy S. Fisher
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Abstract

The average number of constraints per particle $< C_{total} >$ in mechanically stable systems of Platonic solids (except cubes) approaches the isostatic limit at the jamming point ($< C_{total} > \rightarrow 12$), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming chain-like face-face clusters with finite extent form in these systems.

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Kyle C. Smith, Meheboob Alam, Timothy S. Fisher. 2011-06-28. Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids. https://doi.org/10.1103/physreve.84.030301

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