Critical size and internal force analysis of tendril-inspired spontaneous Helicalization mechanism

Abstract

Tendrils initially exhibit straight morphologies before gradually transforming into helical conformations during longitudinal growth. Tendril-inspired helical structures possess advantageous physical properties and functions including versatile morphologies, adaptability, enhanced strength, and scalability. With advancements in nanoscience and nanotechnology, helical architectures across various length scales have been discovered or artificially synthesized. However, the fundamental mechanisms underlying the formation and evolution of helical structures remain elusive. This lack of mechanistic insight has impeded the controlled design and fabrication of helical structures, especially three-dimensional functional devices with integrated helical motifs. Here a mechanical model is systematically proposed for the spontaneous formation of the helical structures, based on the hypothesis of decoupled curling and warping phases. Applying nonlinear elasticity theory, a detailed analysis of the energetics and thermodynamics is presented, accounting for the large deformation that may emerge during planar curling. Additionally, differential relations between internal forces and associated displacements induced by bending and twisting of a slender curved beam under out-of-plane loading are derived, obtaining solutions via Laplace and inverse transforms. The theoretical solutions closely match ex- perimental evidence from shape memory polymers. Furthermore, the theoretical model is utilized to guide the fabrication of the smart helical antenna proposed in our previous work, and discuss the influence of configuration changes on the electromagnetic properties. Elucidating these fundamental mechanisms will facilitate the development of next-generation technologies exploiting helical architectures for diverse applications including flexible electronics, optics, and soft robotics.