Comparison of the Force Network Topology of the 2D and 3D Granular Systems*

In this talk, we present results of discrete element simulations and topological data analysis of the force networks in 2D and 3D compressed granular systems. Our numerical setup consists of the system of cylindrical (2D) or spherical (3D) particles placed on a square or cubical grid inside the box with flat walls. Different initial conditions are guaranteed by random assignment of the particle velocities. System dynamics is driven by isotropic compression of the walls interjected by relaxation period to ensure the independence of compression rate.

Our study focuses on the differences of the force networks for the systems with a different number of dimensions revealing the origins of cluster formation and different percolation properties in 2D and 3D systems. To understand these differences we use the tools of persistent homology and show how the topology of force explain the ridge formation in the systems with different inter-particle force model. Surprisingly, our results suggest a longer lifespan of clusters when the ridge occurs, independently of percolation properties or the number of dimensions.