Overcurvature describes the buckling and folding of rings from curved origami to foldable tents.

Abstract:

:Daily-life foldable items, such as popup tents, the curved origami sculptures exhibited in the Museum of Modern Art of New York, overstrained bicycle wheels, released bilayered microrings and strained cyclic macromolecules, are made of rings buckled or folded in tridimensional saddle shapes. Surprisingly, despite their popularity and their technological and artistic importance, the design of such rings remains essentially empirical. Here we study experimentally the tridimensional buckling of rings on folded paper rings, lithographically processed foldable microrings, human-size wood sculptures or closed arcs of Slinky springs. The general shape adopted by these rings can be described by a single continuous parameter, the overcurvature. An analytical model based on the minimization of the energy of overcurved rings reproduces quantitatively their shape and buckling behaviour. The model also provides guidelines on how to efficiently fold rings for the design of space-saving objects.

journal_name

Nat Commun

journal_title

Nature communications

authors

Mouthuy PO,Coulombier M,Pardoen T,Raskin JP,Jonas AM

doi

10.1038/ncomms2311

subject

Has Abstract

pub_date

2012-01-01 00:00:00

pages

1290

issn

2041-1723

journal_volume

3

pub_type

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