Force Mobilization and Generalized Isostaticity in Jammed Packings of Frictional Grains

TL;DR

This paper investigates the force distribution and isostaticity in 2D frictional sphere packings, revealing that many contacts reach the Coulomb threshold and that these packings exhibit a generalized isostaticity relation, with properties scaling with pressure and friction.

Contribution

It introduces a generalized isostaticity concept for frictional packings, linking fully mobilized contacts to contact number and demonstrating scaling behaviors.

Findings

Approximately half of the contacts are at the Coulomb threshold at low pressure and friction.

Frictional packings follow the generalized isostaticity relation across various friction coefficients.

Contact numbers and packing densities scale with pressure and friction coefficient.

Abstract

We show that in slowly generated 2d packings of frictional spheres, a significant fraction of the friction forces lies at the Coulomb threshold - for small pressure p and friction coefficient mu, about half of the contacts. Interpreting these contacts as constrained leads to a generalized concept of isostaticity, which relates the maximal fraction of fully mobilized contacts and contact number. For p->0, our frictional packings approximately satisfy this relation over the full range of mu. This is in agreement with a previous conjecture that gently built packings should be marginal solids at jamming. In addition, the contact numbers and packing densities scale with both p and mu.