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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) cos 2(θ − π/2) is used to fit the g(r, θ) data. The characteristic lengths and orientations of force networks are then elucidated.