Torsional instabilities and morphology transitions in clamped ribbons under pretension

Abstract

Elastic ribbons possess the capacity to undergo stretching, bending, and twisting, resulting in a diverse range of morphologies. In this study, we conduct both experimental and numerical investigations into the torsional instabilities of clamped ribbons subjected to stretching and twisting loads. The extended Föppl-von Kármán plate model is employed to describe the torsional and tensile responses prior to buckling. Through finite element simulations, we accurately capture the observed evolution of morphologies, spanning from the initial helicoid to a double-layer helicoid, and ultimately to a scrolled yarn structure. As the formation of the double-layer helicoid, the torque, which decreases with the twist during the transverse bending and folding process, gradually increases with the twist until the occurrence of a secondary instability. Furthermore, initial pre-tension enhances the ribbon's capacity to endure torsional deformation, leading to corresponding increases in torque and tension. These findings hold implications for comprehending the intricate deformation mechanisms of slender structures.