Eur. Phys. J. B (2013) 86: 44
https://doi.org/10.1140/epjb/e2012-30445-y

Regular Article

Onset of rigidity in 3D stretched string networks

CSIRO Mathematics, Informatics and Statistics, Private Bag 33, Clayton South, 3168 Melbourne, Australia

^a e-mail: gary.delaney@csiro.au

Received: 4 June 2012
Received in final form: 27 October 2012
Published online: 11 February 2013

Abstract

We extend a previously defined model consisting of connected strings with random natural lengths to three-dimensions [Delaney et al., Europhys. Lett. 72, 990 (2005)]. When this system is expanded, a threshold is reached where a fraction of the strings form a taut network. Further expansion increases the fraction of taut strings up until the point where all strings are taut and the classical problem of a spring network is recovered. We consider a number of string topologies derived from common crystal lattice structures found in nature. We analyze the properties of the system at and above the threshold expansion and demonstrate several unifying features of the model across all lattice structures considered.