Folded and buckled rings
Context :
Rings buckled or folded in tridimensional saddle shapes can be found in daily-life foldable items such as popup tents, laundry baskets and soccer goals; in the curved origami sculptures exhibited in the
Museum of Modern Art of New York; in overstrained bicycle wheels; in released bilayered microrings; or in strained cyclic macromolecules. Surprisingly, despite their popularity and their technological and artistic importance, the design of such rings remained so far essentially empirical.
Our contribution :
We have studied experimentally the buckling and the folding of paper rings as used in curved origami; of rings made of segments of springs; of micro-rings; and even of meter-sized ring sculptures made by tying together arcs of wood. We discovered that the new notion of overcurvature allows us to describe mathematically and physically the general shape of these objects and items. Rings of different overcurvatures from 1 to ~3 are shown below.
Thereby, we also found the best way to fold rings. For those of you who have difficulties in folding back some popup tents after they have been deployed, just look to the animation on the right which shows the energetically-easiest way to fold a ring in three. A video showing how to fold a ring in three is on youtube. A pathway to fold a ring in five is also available here.
The notion of overcurvature and its interest are fully explained in our paper published in Nature Communications. It is an open access article, freely downloadable. And for those of you really interested in the mathematical physics of ring buckling and folding, the supplementary information which accompanies the paper is certainly the best way to go. |
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Collaborations
on this topic are within UCLouvain with Thomas Pardoen on the mechanics of materials, and with Jean-Pierre Raskin and Michaël Coulombier for the fabrication of buckled microrings.
Pierre-Olivier Mouthuy is the FNRS researcher who creatively developed this study when in my group; he now creates artistic LED-based lights within his recently-founded company Odel.