Extent of force indeterminacy in packings of frictional rigid disks

TL;DR

This study uses simulations to analyze how the range of possible contact forces in static packings of frictional particles varies with friction, revealing nonmonotonic behavior and links to stability.

Contribution

It introduces methods to quantify force indeterminacy in frictional packings and explores its dependence on friction coefficient and local force chain properties.

Findings

Force indeterminacy varies nonmonotonically with friction.

Larger indeterminacy correlates with increased robustness to perturbations.

Local indeterminacy is higher on force chains at intermediate friction.

Abstract

Static packings of frictional rigid particles are investigated by means of discrete element simulations. We explore the ensemble of allowed force realizations in the space of contact forces for a given packing structure. We estimate the extent of force indeterminacy with different methods. The indeterminacy exhibits a nonmonotonic dependence on the interparticle friction coefficient. We verify directly that larger force-indeterminacy is accompanied by a more robust behavior against local perturbations. We also investigate the local indeterminacy of individual contact forces. The probability distribution of local indeterminacy changes its shape depending on friction. We find that local indeterminacy tends to be larger on force chains for intermediate friction. This correlation disappears in the large friction limit.