Disclinations, e-cones, and their interactions in extensible sheets

TL;DR

This paper explores the formation and organization of topological defects called e-cones in stretched and twisted elastic sheets, revealing their lattice arrangement, growth behavior, and transition regimes based on tension and elasticity.

Contribution

It uncovers the nucleation, growth, and spatial organization of e-cones in elastic sheets, contrasting them with d-cones, and analyzes the transition from geometric to elastic wavelength regimes.

Findings

Vertices form a triangular lattice of e-cones

Growth of wrinkled width aligns with a far-from-threshold model

Transition from geometry-dominated to elasticity-dominated wavelength regimes

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.