Geometry of Frictionless and Frictional Sphere Packings

TL;DR

This study investigates the structural properties of static sphere packings with and without friction, revealing how friction influences contact numbers and packing stability through molecular dynamics simulations.

Contribution

It provides a detailed analysis of how friction affects the isostatic and hyperstatic nature of sphere packings, highlighting the dependence on system parameters and history.

Findings

Frictionless packings are always isostatic with six contacts.

Frictional packings exhibit a range of hyperstatic states.

Coordination number decreases smoothly from 6 to 4 as friction increases.

Abstract

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $\mu$ between two particles is increased.