Evolution of Force Networks in Dense Particulate Media

Abstract

We introduce novel sets of measures with the goal of describing dynamical properties of force networks in dense particulate systems. The presented approach is based on persistent homology and allows for extracting precise, quantitative measures that describe the evolution of geometric features of the interparticle forces, without necessarily considering the details related to individual contacts between particles. The networks considered emerge from discrete element simulations of two dimensional particulate systems consisting of compressible frictional circular disks. We quantify the evolution of the networks for slowly compressed systems undergoing jamming transition. The main findings include uncovering significant but localized changes of force networks for unjammed systems, global (system-wide) changes as the systems evolve through jamming, to be followed by significantly less dramatic evolution for the jammed states. We consider both connected components, related in loose sense to force chains, and loops, and find that both measures provide a significant insight into the evolution of force networks. In addition to normal, we consider also tangential forces between the particles and find that they evolve in the consistent manner. Consideration of both frictional and frictionless systems leads us to the conclusion that friction plays a significant role in determining the dynamical properties of the considered networks. We find that the proposed approach describes the considered networks in a precise yet tractable manner, allowing to identify novel features which could be difficult or impossible to describe using other approaches.

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• Topological data analysis of continuum percolation with disks
• Topological Persistence Machine of Phase Transitions
• Granular Response to Impact: Topology of the Force Networks
• Structure of force networks in tapped particulate systems of disks and pentagons (Part 1): Clusters and Loops
• Structure of force networks in tapped particulate systems of disks and pentagons (Part 2): Persistence analysis
• Topology of Force Networks in Granular Media under Impact
• Failure of confined granular media due to pullout of an intruder: From force networks to a system wide response
• Force Percolation Transition of Jammed Granular Systems
• Scaling Properties of Force Networks for Compressed Particulate Systems
• Impact-induced hardening in dense frictional suspensions
• Topological Signals of Singularities in Ricci Flow
• Two approaches to quantification of force networks in particulate systems
• Evolution of force networks in dense granular matter close to jamming
• Quantitative Measure of Memory Loss in Complex Spatio-Temporal Systems
• Stochastic methods for slip prediction in a sheared granular system