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Updated: Aug 15, 2026

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires
Published on: July 24, 2018
Force distributions in a triangular lattice of rigid bars
Brian P Tighe1, Joshua E S Socolar, David G Schaeffer
1Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708, USA.
Abstract:
We study the uniformly weighted ensemble of force balanced configurations on a triangular network of nontensile contact forces. For periodic boundary conditions corresponding to isotropic compressive stress, we find that the probability distribution for single-contact forces decays faster than exponentially. This superexponential decay persists in lattices diluted to the rigidity percolation threshold. On the other hand, for anisotropic imposed stresses, a broader tail emerges in the force distribution, becoming a pure exponential in the limit of infinite lattice size and infinitely strong anisotropy.
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