Scale invariance and universality of force networks in static granular matter

TL;DR

This paper demonstrates that force networks in static granular matter exhibit scale invariance and universality, with consistent scaling behavior across different conditions and models, revealing fundamental properties of granular materials.

Contribution

It provides evidence for the scale invariance and universality of force network clusters in granular matter, including a comparison with a generalized statistical ensemble.

Findings

Force networks show scale invariance in cluster sizes.

Universal scaling exponents and functions are observed across conditions.

The flat ensemble model shares the same universality class as real granular packings.

Abstract

Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial processing. Previous studies have focused on the global structure of external forces (the boundary condition), and on the probability distribution of individual contact forces. The disordered spatial structure of the force network, however, has remained elusive so far. Here we report evidence for scale invariance of clusters of particles that interact via relatively strong forces. We analyzed granular packings generated by molecular dynamics simulations mimicking real granular matter; despite the visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, and thus determine a universality class. Remarkably, the flat ensemble of force configurations--a simple generalization of equilibrium statistical mechanics--belongs to the same universality class, while some widely studied simplified models do not.