Topology of force networks in compressed granular media

¹ Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology - Newark, NJ 07102, USA
² Departments of Mechanical Engineering & Materials Science and Physics, Yale University New Haven, CT 06520-8284, USA
³ Department of Mathematics, Rutgers University - Piscataway, NJ 08854-8019, USA
⁴ Department of Physics and Center for Nonlinear and Complex Systems, Duke University Durham, NC 27708-0305, USA

^a kondic@njit.edu

Received: 5 October 2011
Accepted: 25 January 2012

Abstract

Using numerical simulations, we investigate the evolution of the structure of force networks in slowly compressed model granular materials in two spatial dimensions. We quantify the global properties of the force networks using the zeroth Betti number B0, which is a topological invariant. We find that B0 can distinguish among force networks in systems with frictionless vs. frictional disks and varying size distributions. In particular, we show that 1) the force networks in systems composed of frictionless, monodisperse disks differ significantly from those in systems with frictional, polydisperse disks and we isolate the effect (friction, polydispersity) leading to the differences; 2) the structural properties of force networks change as the system passes through the jamming transition; and 3) the force network continues to evolve as the system is compressed above jamming, e.g., the size of connected clusters with forces larger than a given threshold decreases significantly with increasing packing fraction.