Spring curling

We consider the curling of an initially flat but naturally curved elastica on a hard, nonadhesive surface. Combining theory, simulations, and experiments, we find novel behavior, including a constant front velocity and a self-similar shape of the curl that scales in size as t1=3 at long times after the release of one end of the elastica. The front velocity is selected by matching the self-similar solution with a roll of nearly constant curvature located near the free end.


Callan-Jones, A., Brun, P.-T., & Audoly, B. (2012). Self-Similar Curling of a Naturally Curved Elastica. Physical Review Letters, 108(17), 174302. doi:10.1103/PhysRevLett.108.174302