Characterizing Granular Networks Using Topological Metrics

TL;DR

This study compares experimental and numerical granular systems during shear jamming, revealing that topological metrics and the fraction of non-rattler particles universally predict the system's mechanical state.

Contribution

It introduces a comprehensive analysis linking micro, mesoscopic, and macro properties using topological metrics, highlighting their universality and sensitivity to numerical noise.

Findings

Number of particles with at least two contacts predicts system state.

All measures depend on the fraction of non-rattler particles, $f_{NR}$.

Force network topology is affected by numerical force noise.

Abstract

We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range form microscopic, through mesoscopic to system-wide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between micro and macro scales. We report two main findings: the number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress tensor derived measures and contact numbers depend in a universal manner on the fraction of non-rattler particles, $f_{NR}$. The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both $f_{NR}$ and topological metrics are useful measures to consider when quantifying the state of a granular system.