Disclinations, e-cones, and their interactions in extensible sheets.
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.
Gulliver UMR 7083, CNRS, ESPCI ParisTech, PSL Research University, 10 rue Vauquelin F-75005 Paris, France. julien.chopin@espci.fr and Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, 4 place Jussieu, F-75005 Paris, France.
Julien
J
Chopin
Department of Physics, Clark University, 950 Main Street, Worcester, MA 01610, USA. akudrolli@clarku.edu.
Arshad
A
Kudrolli