The frictional pebble game: An algorithm for rigidity percolation in saturated frictional assemblies

We present a fast, robust algorithm to determine rigid and floppy structures in two-dimensional (2D) assemblies of saturated frictional particles, based upon a generalisation (Lee and Streinu (2008) [11]) of the classical pebble game algorithm (Jacobs and Hendrickson (1997) [10]) for frictionless systems. By saturated, we refer to frictional systems for which all particle contacts involve sliding friction, which is relevant for certain frictional models and the study of incipient flow and stress-strain hysteresis. Whilst we do not present a mathematical proof of this method, we demonstrate validity via comparison with results from a classical method based on the network stiffness matrix over a diverse range of particle assemblies, including diluted bond networks and assemblies of cohesive, frictional particles.