A compact mathematic model that explains buckling of structures such as toy springs or foldable tents is described this week in Nature Communications. The research provides an analytical model that accurately describes the folding of rings and related structures into three-dimensional objects.

Although the buckling of objects is largely understood empirically, a compact mathematical theory that is able to describe the folding of objects is much more difficult to achieve. Alain Jonas and colleagues have developed a family of mathematical curves that is able to describe the folding of rings. The three-dimensional buckling of these objects is then described by a mathematical parameter, the overcurvature. The authors demonstrate that the mathematical predictions that they make match very well to experimental results.

The general model derived here is not only relevant to some consumer products, but may also be useful for the understanding of the shape of leaves and petals or even that of some complex molecules.