Elasticity & Rigidity Percolation — Random Networks

A disordered spring network undergoes a rigidity transition as bond density crosses the Maxwell isostatic point. Below threshold: floppy mechanisms; above: rigid elastic solid. Captures the mechanics of gels, glasses, and biological networks.

Random Spring Network

Rigidity Analysis

Bonds / site (z)
Maxwell criterion 2d=4
Floppy modes f
Rigidity