Force distributions in a triangular lattice of rigid bars

TL;DR

This paper investigates force distributions in a triangular lattice of rigid bars, revealing super-exponential decay under isotropic stress and exponential decay under strong anisotropic stress, with implications for understanding force networks.

Contribution

It provides a detailed analysis of force distributions in a triangular lattice under different stress conditions, highlighting the transition from super-exponential to exponential decay.

Findings

Force distribution decays faster than exponential under isotropic stress.

Anisotropic stress leads to a broader, exponential tail in force distribution.

Super-exponential decay persists at the rigidity percolation threshold.

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.