Simple models for granular force networks

TL;DR

This paper reviews theoretical models and analyzes experimental force networks in granular matter, showing that simple geometric models can capture key features of force distribution without detailed force balance considerations.

Contribution

It introduces a simple graph-based algorithm to analyze granular force networks and compares experimental data with geometric models like percolation, highlighting their similarities.

Findings

Force networks are highly inhomogeneous with force chains.

Simple geometric models can replicate the spatial distribution of force networks.

Force balance constraints are not always necessary to describe network geometry.

Abstract

A remarkable feature of static granular matter is the distribution of force along intricate networks. Even regular inter-particle contact networks produce wildly inhomogeneous force networks where certain "chains" of particles carry forces far larger than the mean. In this paper, we briefly review past theoretical approaches to understanding the geometry of force networks. We then investigate the structure of experimentally-obtained granular force networks using a simple algorithm to obtain corresponding graphs. We compare our observations with the results of geometric models, including random bond percolation, which show similar spatial distributions without enforcing vector force balance. Our findings suggest that some aspects of the mean geometry of granular force networks may be captured by these simple descriptions.