Mechanics and topology of twisted hyperelastic filaments under prescribed elongations: Experiment, theory, and simulation

Abstract

Soft filaments can be stretched, bent, and twisted, exhibiting complex configurations. When a filament undergoes large torsional deformation, it can display instabilities, and its post-buckling behavior and configuration evolution differs significantly from that observed under small deformation. We study the mechanics and topologically complex morphologies of twisted rubber filaments under prescribed elongation by combining experiment and finite strain theory. Based on the Mooney-Rivlin model, a finite strain theory of the hyperelastic filament under combined tension, bending, and torsion has been established, accounting for both geometrical and material nonlinearities. An experimental and theoretical morphological phase diagram is constructed as a function of the twist density and the initial elongation. The buckling and post-buckling behaviors of the twisted rubber filaments under prescribed elongation are well captured by the theory that considers geometrical nonlinearity and self-contact. By tracking the interconversion of link, twist, and writhe, we accurately determine the configuration and the critical points of phase transitions. The theoretical predictions agree closely with the measurements. This work sheds light on understanding the morphological complexity of the loaded hyperelastic rod.