Twisting and braiding elastic filament pairs*

Twisting and braiding filaments is a fundamental topological transformation relevant to making ropes, tying shoelaces, robotics, and the mechanical properties of entangled polymers. The regime of inextensible, infinitely thin filaments has been studied extensively, especially in the context of knots. Here, we investigate with experiments the elastic energy required to twist a filament-pair while prescribing the initial pre-stretch. First, we show that the torque profile with applied twist is non-monotonic, with a maximum that depends on their initial length, separation distance, and pre-stretch. After the filaments cross and come in contact, the torque is measured to increase quasi linearly while the filaments form a double helix in a central region which grow in length with increasing twist. We develop a nonlinear elasto-geometric model that captures quantitatively the full torque profile, and the evolution of the filament braid with twist. We find that the combined effect of geometrical nonlinearties with large stretching and self-twist make significant contributions, while bending and contact deformation make only perturbative contributions to the overall response.