Onset of rigidity for stretched string networks

Abstract

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. Show more