Stability and jamming transition in hard granular materials: Algebraic graph theory

Abstract

Dry granular matter is modelled as a graph of grains linked by purely repulsive contacts. Its stability (jamming) is insured by odd circuits that prevent the grains from rolling on each other. A topological dynamical matrix is associated with the graph; it has a spectrum of low-energy excitations characteristic of dry, disordered granular matter. In the limit of large stiffness-to load ratio, dry granular matter has two possible dynamical states, dry fluid and jammed, rigid but fragile solid. © 2009 Springer-Verlag Berlin Heidelberg.