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Force distributions in a triangular lattice of rigid bars

Brian P. Tighe·Joshua E. S. Socolar·David G. Schaeffer·W. Garrett Mitchener·Mark L. Huber
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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 super-exponential 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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Brian P. Tighe, Joshua E. S. Socolar, David G. Schaeffer, W. Garrett Mitchener, Mark L. Huber. 2005-07-26. Force distributions in a triangular lattice of rigid bars. https://doi.org/10.1103/physreve.72.031306

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