Shape-shift and Surf: Propulsion via Bending

Stresses arising from curvature mismatches can result in propulsive net forces and torques. Frustrated elastic objects move along gradients in intrinsic curvature [1] and, on fluid membranes, meniscus-climbing insects generate curvature mismatches via capillary disturbances [2]. Inspired by such propulsion mechanisms, we consider a "surfer"– an elastic object consisting of two inextensible strips with non-zero bending moduli attached at their midpoints. When confined to a generic curved surface, the surfer is attracted towards elliptical or hyperbolic curves surrounding umbilical points of the surface. Further, the umbilic couples the surfer's rotational and translational motions leading the surfer to traverse these entrapment curves when an external torque is applied. This non-reciprocal coupling combined with entrapment enables navigation between umbilics, allowing the surfer to chart courses across arbitrary curved surfaces.



[1] H. Aharoni, J. M. Kolinski, M. Moshe, I. Meirzada, and E. Sharon, Internal stresses lead to net forces and torques on extended elastic bodies, Phys. Rev. Lett. 117, 124101 (2016).



[2] Hu, D., Bush, J. Meniscus-climbing insects. Nature 437, 733–736 (2005).