Twist-induced Buckling Instability and Morphological Phase Transitions in Hyperelastic Filaments

Under large torsional deformation, hyperelastic filaments exhibit spontaneous knotting and complex morphological transitions, particularly under axial loads and self-contact. However, the post-buckling behavior and configuration evolution of the hyperelastic filament differ significantly from those observed under small deformation, particularly when self-contact is considered. Here, we develop a numerical framework combining Cosserat rod theory and Mooney-Rivlin hyperelasticity to simulate buckling and post-buckling behaviors of hyperelastic filaments under torsion, explicitly resolving self-contact via a centerline-based discretization. Torsional experiments on rubber filaments under given axial loads are performed to validate the numerical results. The model successfully predicts the buckling and post-buckling behaviors of twisted rubber filaments under prescribed axial loads. A unified morphological phase diagram, mapping five distinct configurations (straight, localized helix, plectoneme, solenoid, mixed), is experimentally validated and theoretically predicted. This work provides insights into comprehending the intricate morphological nature of constrained soft rods.