Unjamming of Granular Packings due to Local Perturbations: Stability and Decay of Displacements

TL;DR

This study investigates how local perturbations cause displacements in jammed granular packings, revealing nonmonotonic effects of friction on stability and displacement decay, with implications for understanding force networks.

Contribution

It provides new insights into the friction-dependent behavior of force indeterminacy and critical forces in jammed granular materials through simulations.

Findings

Displacements decay as a power law with distance from perturbation.

Critical force and decay exponent show nonmonotonic dependence on friction.

Maximum response occurs at a friction coefficient of 0.1.

Abstract

We study the mechanical response generated by local deformations in jammed packings of rigid disks. Based on discrete element simulations we determine the critical force of the local perturbation that is needed to break the mechanical equilibrium and examine the generated displacement field. Displacements decay as a power law of the distance from the perturbation point. The decay exponent and the critical force exhibit nontrivial dependence on the friction: Both quantities are nonmonotonic and have a sharp maximum at the friction coefficient 0.1. We find that the mechanical response properties are closely related to the problem of force-indeterminacy where similar nonmonotonic behavior was observed previously. We establish direct connection between the critical force and the ensemble of static force networks.