Stretching an Elastic Loop: Crease, Helicoid, and Pop Out.

Abstract

Under geometric constraints, a thin structure can respond to an external loading in an unexpected way. A paper strip that is looped and pulled can be used for simple experimentation of such a process. Here, we study this seemingly very simple phenomenon in detail by combing experiments and theory. We identify the three types of shape transitions, i.e., crease, helicoid, and pop out, from a stretched loop, and classify them in terms of parameters characterizing a ribbon geometry. We establish a transition-type diagram by compiling our extensive experimental data. Numerical simulations based on the Kirchhoff rod theory and scaling argument reveal that the pop-out transition is governed by a single characteristic length ξ∼b^{2}/h, where b and h are the ribbon's width and thickness, respectively. We also reveal the key roles of other physical effects such as the anisotropy of the bending elasticity and plastic deformations upon the shape selection mechanisms of a constraint ribbon.