Tail of the contact force distribution in static granular materials

Abstract

We numerically study the distribution P (f) of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling to resolve the asymptotic decay of P (f) for large f, and determine P (f) down to values of order 10-45 for ordered and disordered systems in two (2D) and three dimensions (3D). Our findings unambiguously show that, in the ensemble approach, the force distributions decay much faster than exponentially: P (f) ∼exp (-c fα), with α 2.0 for 2D systems, and α 1.7 for 3D systems. © 2007 The American Physical Society.