Rigid cluster decomposition reveals criticality in frictional jamming

TL;DR

This paper applies rigidity percolation theory to frictional jamming, revealing a second-order transition characterized by the emergence of a system-spanning rigid cluster and critical cluster size distribution, contrasting with frictionless jamming.

Contribution

It introduces a generalized pebble game for frictional contacts and demonstrates a critical transition in rigid cluster formation during shear-induced jamming.

Findings

Identification of a second-order transition in frictional jamming.

Discovery of a critical cluster size distribution at the transition.

Rigid clusters correlate with measures of rigidity.

Abstract

We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. We discover a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.