Betweenness Centrality as Predictor for Forces in Granular Packings

Abstract

A load applied to a jammed frictional granular system will be localized into a network of force chains making inter-particle connections throughout the system. Because such systems are typically under-constrained, the observed force network is not unique to a given particle configuration, but instead varies upon repeated formation. In this paper, we examine the ensemble of force chain configurations created under repeated assembly in order to develop tools to statistically forecast the observed force network. In experiments on a gently suspended 2D layer of photoelastic particles, we subject the assembly to hundreds of repeated cyclic compressions. As expected, we observe the non-unique nature of the force network, which differs for each compression cycle, by measuring all vector inter-particle contact forces using our open source PeGS software. We find that total pressure on each particle in the system correlates to its betweenness centrality value extracted from the geometric contact network. Thus, the mesoscale network structure is a key control on individual particle pressures.