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Latent sculpture in a curved crease
Thin sheets have an inherent tendency to shape themselves. When forced, they seek to deform in a way that bends without stretching. Thus a crushed sheet shapes itself into a crumpled shape made of flat facets bounded by sharp edges. These sharp features fail to avoid stretching : the deformation energy of stretching is comparable to that of bending. Yet gentle interventions can guide the sheet into deterministic shapes whose energy is virtually all due to bending. One way to guide a flat sheet is to draw a curve on it and then crease it along the curve. As the crease angle increases from zero, the sheet rises into space to form a shape determined by the curve and the crease angle. We recall the two established rules that determine the spatial shape. Next we ask whether a finite crease line can shape an infinite sheet. The PhD work of Aaron Mowitz shows that many such shapes are possible, and they can form at modest cost in energy. Another student Anshuman Pal has identified a simple form of radial wrinkling that wrinkles without stretching. A simple geometric Ansatz explains the energy cost of a wide range of deformations.
