Critical jamming of frictional grains in the generalized isostaticity picture

TL;DR

This paper investigates the vibrational properties of frictional grains near jamming, introducing a generalized isostaticity framework that accounts for slipping contacts, revealing a plateau in the density of states and a smooth frictionless limit.

Contribution

It introduces a generalized isostaticity concept considering slipping contacts, clarifying vibrational behavior and the nature of the frictionless limit in frictional jamming.

Findings

Vibrational density of states exhibits a plateau near the generalized isostaticity line.

Crossover frequency scales linearly with distance from the isostaticity line.

Frictionless limit becomes smooth when fully mobilized contacts are allowed to slip.

Abstract

While frictionless spheres at jamming are isostatic, frictional spheres at jamming are not. As a result, frictional spheres near jamming do not necessarily exhibit an excess of soft modes. However, a generalized form of isostaticity can be introduced if fully mobilized contacts at the Coulomb friction threshold are considered as slipping contacts. We show here that, in this framework, the vibrational density of states (DOS) of frictional discs exhibits a plateau when the generalized isostaticity line is approached. The crossover frequency to elastic behavior scales linearly with the distance from this line. Moreover, we show that the frictionless limit, which appears singular when fully mobilized contacts are treated elastically, becomes smooth when fully mobilized contacts are allowed to slip.