Onset of rigidity in 3D stretched string networks
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- Delaney, G.W. & Khoury, D. Eur. Phys. J. B (2013) 86: 44. doi:10.1140/epjb/e2012-30445-y
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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.