Health & Medicine / Aging

Renaissance artists worked hard on their wrinkles. Rich garments cascading in complex folds over knee, elbow, and buttock evoked the bodies they concealed—and sometimes something more. “The restless activity of the drapery, like the quivering of the fingers and the rippling descent of the curls, carries a new kind of feverish emotion,” the art historian Frederick Hart once wrote about Andrea del Verrocchio’s sculpture of Doubting Thomas. Wrinkles in the Renaissance were frozen lines of energy, psychic as well as kinetic; getting the wrinkles right in a scene helped the artist get the energy right. Not incidentally, it also showed what an accomplished artist he was.

Prescientifics that they were, however, the Renaissance masters did not fully understand the physical laws of wrinkling. “They were depicting reality, which is very different from trying to understand it,” says Lakshminarayanan Mahadevan, a physicist at Harvard University. Mahadevan thinks he has a handle on wrinkles—he and physicist Enrique Cerda at Cambridge University in England recently proposed a “general theory of wrinkling.” If you know the dimensions of the fabric and the forces acting on it, the theory predicts the amplitude and the wavelength of the resulting wrinkles—that is, how big and how far apart they will be. And it works not only for cloth, plastic wrap, and other fabrics but also for shriveled apples and people’s faces.

A thin sheet of fabric or tissue, Mahadevan says, is like a spring: When you deform it, it stores elastic energy. The sheet can deform either by stretching or by bending. Being thin, it is typically less resistant to bending. The energy in a spring or in a stretched sheet is proportional to the strain from stretching squared, but the energy in a bent sheet is proportional to the curvature squared. A sheet with lots of little wrinkles contains more curvature and thus more bending energy than a sheet with one big wrinkle. It was the 18th-century Swiss mathematician Leonhard Euler who first realized this, and who also had the fundamental insight that underlies all wrinkle physics today: A deformed sheet adopts the shape that minimizes its total bending energy.

One way to deform a thin sheet of paper, for example, is to compress it from all sides. Technically that’s called crumpling, and a team at the University of Chicago led by physicist Tom Witten has been studying the process for years. The energy you add to a sheet as you crumple it, they have found, causes it to buckle along a series of sharp ridges. Conversely, as you uncrumple the paper—or a candy wrapper—some of the elastic energy comes out again as a series of cracking sounds.

In neither direction does the process go smoothly. As you crumple a piece of paper, it takes quantum jumps into new conformations, each one close to the lowest-energy state it can adopt under the applied force. The process can continue for a surprisingly long time. Witten and his colleague Sidney Nagel recently stuffed a sheet of Mylar eight inches in diameter into a tube four inches in diameter, then set a half-pound piston on top. After three weeks, the sheet was crumpled into a disk a tenth of an inch thick—and it still hadn’t reached a stable state.