Analyzing the Rigidity of Force Networks in Jammed Granular Packings*

An understanding of the rigidity of granular systems necessitates the extension of the concept of a mechanical network to include an abstract force-space network. Contact forces between dry grains in mechanical equilibrium can be represented in a dual force space as a network of edges that form a tiling. This force tiling paradigm has been found to be particularly useful in the characterization of stress-induced transitions in granular materials. As a generic network itself, the force tiling network can be studied using techniques used in the investigation of more conventional networks.

We analyze the rigidity of generic force networks obtained from simulations, which provides insight into network properties including rigid and over-constrained regions as well as a counting of zero modes. We exploit the duality between the real-space contact network and the force tiling to then connect this analysis to physical properties of jammed packings. This provides improved understanding of the stability of granular systems against the effect of external perturbations.