Physics Behind the Snapping of a Twisted Balloon

It is childhood experience to twist balloons and turn them into dogs and flower. In this talk we investigate the process that leads up to the snap of a cylindrical balloon. For a twisted short balloon (1<L/D<7 where L, D : length and diameter), its phase transits from (1) being sheared and wrinkle-free while torque (τ) is linear to θ, (2) appearance of a neck without wrinkles, while radius and shear angle are found to obey r³dθ/dx=const, (3) development of parallel wrinkles whose number ~12 is insensitive to L, D, and thickness. τ increases concavely with θ, to (4) wrinkles cross one another eventually and are followed by a sudden snap into two segments, as for a bended drinking straw. For a medium-size balloon (7<L/D<15), (a) similar to (1), (b) skip (2, 3) to become curled with a low-amplitude oscillation in θ, (c) similar to (4). When the balloon is long (15<L/D), (i) similar to (1) (ii) similar to (b), but develop a supercoil while accompanied by a suddenly drop in τ, (iii) repeat (i, ii). Heuristic models are proposed to understand the physics behind different phases. MD simulation is also performed to reveal energetics. Furthermore, to verify whether the above properties are unique to a quasi-1D object (balloons), a thread (real 1D) and ribbon (2D) are also studied.