Topological signatures of jamming in granular force networks via persistent homology

TL;DR

This paper uses persistent homology to analyze force networks in granular materials, revealing structural transitions around jamming that enhance understanding of system stability.

Contribution

It introduces a topological framework to characterize force networks in granular materials, capturing critical connectivity changes during jamming.

Findings

Identified topological signatures associated with jamming transition.

Distinguished different phases of particle interactions.

Revealed structural transitions in force networks.

Abstract

Granular materials exhibit intricate force networks, often concentrated in chains rather than being uniformly distributed. These meso-scale structures are complex to characterize, owing to their heterogeneous and anisotropic nature. We present a topological analysis in which we characterize force networks by studying the connectivity of contact forces in granular materials. We obtain the force network data during the isotropic compression of a 2D granular ensemble, which comprises of bidisperse photoelastic disks. The force chains are visualized using a bright-field polariscope, which are then analyzed using photoelasticity techniques to get contact force information across all the particles in the granular ensemble. The forces and contact network are studied using topological descriptors. We analyze the evolution of these descriptors using methods developed in the areas of computational topology and persistent homology. Specifically, we evaluate the number of homology class generators to capture critical changes in network connectivity with the evolution of packing fraction. Building on previous applications of persistent homology, our topological analysis of the force network provides valuable insights by distinguishing different phases of particle interactions and revealing unique structural transitions around jamming and thus help enhance our understanding of the stability and jamming dynamics in granular systems.