Onset of rigidity for stretched string networks

We define and analyse an elementary model for a network of strings with random natural lengths. As this system is expanded, a threshold is reached where some of the strings form a taut string network. Further expansion increases the fraction of taut strings, until eventually all strings are taut and the classical problem of a spring network is recovered. Here we provide an analysis of the properties of the system at and beyond the threshold expansion, relating results to the expectations of constraint theory.