“It was as if they wrote the solicitation just for us,” says Christian Santangelo, a physicist at the University of Massachusetts Amherst and a co-principal investigator on an ODISSEI proposal. Along with two origami artists and an expert in origami mathematics, Santangelo and his colleague Ryan Hayward, a chemical engineer at Amherst who specializes in polymers, are proposing a new kind of three-dimensional (3D) printer. Instead of slowly building an object with layers and layers of polymer, as current 3D printers do, they would print a flat polymer sheet with a two-dimensional (2D) origami-like pattern, then force it to fold into a close approximation of the desired 3D object.
One part of the project will involve refining a computer program developed by one of the origami artists, physicist Robert Lang of Alamo, California. Given a desired shape, the program will generate a diagram of the required fold pattern. At present, the program states only whether a particular fold on a sheet should be convex (in origami terms, a mountain fold) or concave (a valley fold). The user still has to devise a sequence of manipulations that can achieve those folds and create the figure. But the kinds of folding required by the project could quickly reach such levels of complexity that a human solution would be impossible. What the researchers foresee instead is a completely automated process in which a 2D sheet is inscribed with a computer-generated pattern of instabilities, and then folds correctly in one smooth, coordinated motion.
Unfortunately, in Hayward's experiments so far, the folds just buckle into mountains or valleys at random. A potential solution may lie in the wavy-leaf-edge phenomenon, says Santangelo. If cells along the edge of a growing plant leaf multiply faster than those in the interior, he explains, they run out of room to lie smoothly in a plane, and the leaf edge is forced to ripple to accommodate them. If he and Hayward can work out how to make the polymer sheet swell in a way that varies from point to point, they could produce a complex pattern of rippling and curling that would help to control the sheet's folding.
Just as natural phenomena can inform extreme mechanics, the discipline's researchers can also use their knowledge to explain peculiarities in natural structures. “This field is filled with small secrets,” says Pedro Reis, an engineer at the Massachusetts Institute of Technology in Cambridge and one of the leaders of the movement.
Take the mechanisms at work in a grain of pollen, for example. Reis pulls out a small torpedo-like shape made of a light green, rubbery material. He stretches it, then crushes it in his fist. A pollen grain undergoes torture, he says: it gets wet, swells, dries out and is crushed, so plants have evolved strategies such as built-in soft spots to help their pollen to avoid damage. Reis pokes a dimple in the torpedo. Scientists can learn from this that a shell with a soft spot is more resistant to failure than one that is completely rigid, he says. “We are trying to learn from nature. How it evolved to deal with these problems for which we have no intuition is very inspiring.”
Reis sets the torpedo aside and, twisting an imaginary string between his fingers, moves on to the subject of the sea-floor cables that carry Internet traffic around the globe. Mechanical instabilities can cause complex behavior in these structures, too, he says. Lay too much cable, and it will curl and kink, resulting in poor signal quality. Lay too little, and the line will be tense and vulnerable to snapping. When a ship dragging its anchor sliced through one such cable in February, six countries in East Africa lost Internet connectivity. Although a better understanding of long, thin objects' instabilities wouldn't have prevented the accident, Reis says, it might have made for a cable more resilient to breakage. An improved theory of cables could also be of great use to fields ranging from the oil industry to the mechanics of DNA.