Shape selection and multi-stability in helical ribbons

Abstract

Helical structures, almost ubiquitous in biological systems, have inspired the design and manufacturing of helical devices with applications in nanoelecromechanical systems, morphing structures, optoelectronics, micro-robotics, and drug delivery devices. Meanwhile, multi-stable structures, represented by the Venus flytrap and slap bracelet, have attracted increasing attention due to their applications in making artificial muscles, bio-inspired robots, deployable aerospace components, and energy harvesting devices. Here we show that the mechanical anisotropy pertinent to helical deformation, together with geometric nonlinearity associated with multi-stability, can lead to a selection principle of the geometric shape and multi-stability in spontaneous helical ribbons. Simple table-top experiments were also performed to illustrate the working principle. Our work will promote understanding of spontaneous curling, twisting, wrinkling of thin objects, and their instabilities. The proposed theoretical framework can also serve as a tool for developing functional structures and devices featuring tunable, morphing geometries and smart actuation mechanisms that can be applied in a spectrum of areas.