MERCI: Mixed Curvature-Based Elements for Computing Equilibria of Thin Elastic Ribbons

Fig. 1. A Wunderlich thin elastic ribbon (in blue, computed with our Meaci code) does not deform like a rectangular Kirchhoff thin elastic rod (in red, computed (left) as a flat super-clothoid, and (right) with a shooting technique). Left: Starting from the exact same curly natural shape (in gray), the configuration of the ribbon under its own weight substantially diverges from that of the rod even though both have the same rectangular cross-section and the same clamping orientation. Right: Noticeable differences also appear in a clamped-clamped scenario where the ribbon/rod (with w/L = 1/12) is twisted by a half-turn (from top to bottom). In these two scenarios, while the centreline of the rod remains inextensible, its surface stretches too much to represent a ribbon correctly. Note that as the ribbon and the rod possess two distinct equilibria in both scenarios, we make sure to have them buckle "on the same side" to be able to compare their geometry in a meaningful way.