The Duality of Networks in Jammed Granular Packings*

Contact networks in jammed granular systems, derived from contact forces between dry grains in mechanical equilibrium, can be represented in a dual force space as a network of edges that form a space-filling 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 network can be studied with techniques used in the investigation of more conventional networks.

Using jammed granular packings obtained from simulations, we explore the duality between the resultant real-space contact networks and force tilings. We analyze the relationship between zero modes and states of self-stress in these dual networks, and connect it to physical properties of jammed packings and to unjamming. In particular, this can provide improved understanding of the stability of granular systems against the effect of external perturbations.