Force distributions in a triangular lattice of rigid bars

Area of Science:

• Physics
• Materials Science
• Network Science

Background:

• Understanding force distribution in complex networks is crucial for material stability.
• Nontensile contact forces in granular materials and engineered structures exhibit unique behaviors.
• Network geometry significantly influences mechanical properties.

Purpose of the Study:

• To analyze the probability distribution of single-contact forces in uniformly weighted triangular networks.
• To investigate how isotropic and anisotropic stresses affect force distributions.
• To examine the impact of lattice dilution to the rigidity percolation threshold on force distributions.

Main Methods:

• Simulating uniformly weighted ensembles of force-balanced configurations.
• Applying periodic boundary conditions for isotropic compressive stress.
• Imposing anisotropic stresses on triangular lattices.
• Analyzing force distributions in both intact and diluted lattices.

Main Results:

• Under isotropic stress, single-contact force distributions exhibit superexponential decay.
• This superexponential decay is maintained in lattices diluted to the rigidity percolation threshold.
• Anisotropic stresses induce a broader tail in the force distribution, approaching exponential decay in the infinite size/anisotropy limit.

Conclusions:

• The nature of applied stress (isotropic vs. anisotropic) fundamentally alters force distribution tails in these networks.
• Lattice dilution to the rigidity percolation threshold does not change the superexponential decay under isotropic stress.
• The transition to exponential decay under anisotropic stress highlights critical behaviors at large scales and high anisotropy.