The curves and folds of a flower, the wrinkling of our skin, and the wavy edge of torn plastic are among the countless examples of patterns that emerge from the physics of thin elastic sheets. As cells grow nonuniformly in a petal, say, or as ripped plastic deforms along its edge, stresses build up. To accommodate the deformation and relieve the stress, the material has to either compress internally or bend. Both distortions cost energy, but which one Nature chooses depends directly on thickness: The thinner the sheet, the cheaper it is to buckle out of the plane.
For the past decade, researchers have been striving to translate that competition between compression and bending into practical strategies for controlling the shape of a thin film embedded in our three-dimensional world. The mechanism by which in-plane stresses actually break a sheet’s local symmetry is subtle, mathematically formidable, and not entirely understood....
