Force indeterminacy in the jammed state of hard disks

TL;DR

This paper investigates force indeterminacy in jammed hard disk packings using contact dynamics, revealing how force fluctuations depend on friction and their implications for granular material behavior.

Contribution

It introduces a detailed analysis of force fluctuations in granular packings, highlighting the non-monotonous friction dependence and the role of contact network connectivity.

Findings

Force fluctuations vanish at zero friction due to isostaticity.

Force fluctuation magnitude varies non-monotonously with friction.

Increased friction reduces contact network connectivity, affecting force indeterminacy.

Abstract

Granular packings of hard discs are investigated by means of contact dynamics which is an appropriate technique to explore the allowed force-realizations in the space of contact forces. Configurations are generated for given values of the friction coefficient, and then an ensemble of equilibrium forces is found for fixed contacts. We study the force fluctuations within this ensemble. In the limit of zero friction the fluctuations vanish in accordance with the isostaticity of the packing. The magnitude of the fluctuations has a non-monotonous friction dependence. The increase for small friction can be attributed to the opening of the angle of the Coulomb cone, while the decrease as friction increases is due to the reduction of connectivity of the contact-network, leading to local, independent clusters of indeterminacy. We discuss the relevance of indeterminacy to packings of deformable particles and to the mechanical response properties.