Structure of force networks in tapped particulate systems of disks and pentagons (Part 1): Clusters and Loops

TL;DR

This study investigates the topology of force networks in two-dimensional tapped granular systems composed of disks and pentagons, revealing differences in heterogeneity and network structure based on particle shape and force thresholds.

Contribution

It introduces a topological analysis of force networks in granular packings with different particle shapes, highlighting shape-dependent heterogeneity and network features.

Findings

Force networks are more heterogeneous for disks than pentagons.

Number of clusters and loops varies with force thresholds and particle shape.

Simple topological invariants cannot distinguish states with similar packing fractions.

Abstract

The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this paper we consider two dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network's topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.