Isostaticity at Frictional Jamming

TL;DR

This study investigates how mesoscale asperity interactions influence the isostaticity and mechanical properties of frictional granular packings, revealing that proper modeling of asperities leads to isostatic packings at jamming.

Contribution

The paper demonstrates that incorporating mesoscale asperity interactions results in isostatic frictional packings, contrasting with traditional hyperstatic models, and highlights the importance of asperity-based forces in granular physics.

Findings

Frictional packings become isostatic when asperity interactions are considered.

Transition from frictionless to frictional behavior correlates with contact type changes.

Vibrational density of states peak disappears at the isostatic point.

Abstract

Amorphous packings of frictionless, spherical particles are isostatic at jamming onset, with the number of constraints (contacts) equal to the number of degrees of freedom. Their structural and mechanical properties are controlled by the interparticle contact network. In contrast, amorphous packings of frictional particles are typically hyperstatic at jamming onset. We perform extensive numerical simulations in two dimensions of the geometrical asperity (GA) model for static friction, to further investigate the role of isostaticity. In the GA model, interparticle forces are obtained by summing up purely repulsive central forces between periodically spaced circular asperities on contacting grains. We compare the packing fraction, contact number, mobilization distribution, and vibrational density of states using the GA model to those generated using the Cundall-Strack (CS) approach. We find that static packings of frictional disks obtained from the GA model are mechanically stable and isostatic when we consider interactions between asperities on contacting particles. The crossover in the structural and mechanical properties of static packings from frictionless to frictional behavior as a function of the static friction coefficient coincides with a change in the type of interparticle contacts and the disappearance of a peak in the density of vibrational modes for the GA model. These results emphasize that mesoscale features of the model for static friction play an important role in determining the properties of granular packings.