Researchers at MIT now have a mathematical model that knows exactly how wrinkles form on curved surfaces, including on shapes such as raisins, human fingerprints and even the brain.
For example, when a grape dries out and wrinkles up into a raisin, MIT's algorithm can predict exactly what those wrinkles will look like and where they will form.
The same goes for fingerprints. Although each set seems random, they formed that way for a reason.
"If you look at skin, there's a harder layer of tissue, and underneath is a softer layer, and you see these wrinkling patterns that make fingerprints," says Jörn Dunkel, assistant professor of mathematics at MIT. "Could you, in principle, predict these patterns? It's a complicated system, but there seems to be something generic going on, because you see very similar patterns over a huge range of scales."
A previous experiment at the university looked at balls of polymer and studied patterns on those spheres and how air affected those patterns. After beginning to suck air out of the balls, the shapes dimpled, at first creating hexagon patterns. But after removing more air from the balls, the patterns became more convoluted, similar to the patterns in fingerprints.
At the time, there were no theories explaining why this occurs.
However, researchers developed a new mathematical equation about those patterns, combining ideas from both fluid mechanics and elasticity theories. Computer simulations using this equation showed that the mathematical model correctly predicted surface patterns seen in earlier experiments. Researchers also uncovered those very things that affect how wrinkles form.
The mathematical models showed that the curvature of a surface plays a large role in how a surface wrinkles. More curve means a more regular wrinkling. Thickness, too, of an object's shell affects patterning, with thicker shells forming hexagons and thinner shells forming complex fingerprint-like patterns. Considering the earlier experiment with the polymer ball, the shell was thickest with more air removed from inside it.
Although this might seem like strictly theoretical work, this algorithm could be used for more practical applications. It's possible this algorithm could act as a tool for designers to create objects with surfaces that morph.
"This theory allows us to go and look at shapes other than spheres," says Pedro Reis, Gilbert W. Winslow Career Development Associate Professor in Civil Engineering, who did the initial experiments with polymer balls. "If you want to make a more complicated object wrinkle - say, a Pringle-shaped area with multiple curvatures - would the same equation still apply?"
