Disclinations, e-cones, and their interactions in extensible sheets
Abstract
We investigate the nucleation, growth, and spatial organization of topological defects with a ribbon shaped elastic sheet which is stretched and twisted. Singularities are found to spontaneously arrange in a triangular lattice in the form of vertices connected by stretched ridges that result in a self-rigidified structure. The vertices are shown to be negative disclinations or e-cones which occur in sheets with negative Gaussian curvature, in contrast with d-cones in sheets with zero-Gaussian curvature. We find the growth of the wrinkled width of the ribbon to be consistent with a far-from-threshold approach assuming a compression-free base state. The system is found to show a transition from a regime where the wavelength is given by the ribbon geometry, to where it is given by its elasticity as a function of the ratio of the applied tension to the elastic modulus and cross-sectional area of the ribbon.
Cite
@article{arxiv.1601.00575,
title = {Disclinations, e-cones, and their interactions in extensible sheets},
author = {Julien Chopin and Arshad Kudrolli},
journal= {arXiv preprint arXiv:1601.00575},
year = {2016}
}