A Pair Correlation Function Characterizing the Anisotropy of Force Networks

Force networks may underlie the constitutive relations among granular solids and granular flows and inter-state transitions. However, it is difficult to effectively describe the anisotropy of force networks. We propose a new pair correlation function g(r,θ) to describe the characteristic lengths and orientations of force chains that are composed of particles with contact forces greater than the threshold values. A formulation g(r,θ)≈a(r)+b(r)cos2(θ−π/2) is used to fit the g(r,θ) data. The characteristic lengths and orientations of force networks are then elucidated.