Recent advances in material science stimulated research of shape-morphing structures. The simplest strategy towards such structures is a unidirectional bending of a beam. However, the morphologies obtained by these devices are very limited.
In this work, we study a slight variation of this concept: a curved ribbon with spontaneous curvature in its radial direction. We find this structure to be geometrically frustrated, i.e., to have no stress-free configuration. Furthermore, its shape depends heavily on its thickness and width, transitioning from a toroidal smooth shape to a polygonal tube.
We show that this shape transition differs from other shape transitions known in frustrated thin sheets. Moreover, the polygonal structures exhibit mechanical stress that is focused at their corner, a rare property in free-forming structures.
Finally, we present two different experimental techniques to manufacture such structures, and our experimental results agree very well with the theory. We expect these novel structures to play a significant role in engineering applications and to appear in natural systems.
E. Siéfert, I. Levin, and E. Sharon, Euclidean Frustrated Ribbons. Phys. Rev. X 2021 11
I. Levin, E. Siéfert, E. Sharon, and C. Maor, Hierarchy of Geometrical Frustration in Elastic Ribbons: shape-transitions and energy scaling obtained from a general asymptotic theory JMPS 156 104579 (2021)