Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids

TL;DR

This study investigates the isostaticity of constraints in jammed systems of Platonic solids, revealing that while the average constraints approach the isostatic limit, the contact number remains hypostatic, with local order influencing constraint formation.

Contribution

It introduces angular alignment metrics to classify constraints and links local orientational order to the emergence of constraints in jammed Platonic solids.

Findings

Average constraints approach the isostatic limit at jamming.

Contacts are hypostatic despite constraints reaching the isostatic limit.

Face-face clusters form with finite extent at jamming.

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.