Wrinkles prediction prelude to morphing materials?

A team from the Massachusetts Institute of Technology (MIT) in the US has developed a theory that predicts how wrinkles on curved surfaces occur and take shape.

Jörn Dunkel, an assistant professor of mathematics at MIT, said: "It's a complicated system, but there seems to be something generic going on because you see very similar patterns over a range of scales."

According to Dunkel, there exists a mathematical framework for describing wrinkling in the form of elasticity theory, a complex set of equations to predict the resulting shapes in computer simulations. While these equations are far too complicated to pinpoint exactly when certain patterns start to morph, (let alone what causes such morphing) by combining ideas from fluid mechanics with elasticity theory, the team derived a simplified equation that can accurately predict wrinkling patterns.

Dunkel explained: "What type of stretching and bending is going on, and how the substrate underneath influences the pattern — all these different effects are combined in coefficients so you now have an analytically tractable equation that predicts how the patterns evolve, depending on the forces that act on that surface."

Curvature is one major determinant. The more curved an object, the more regular its wrinkled surface. The thickness of an object's shell also plays a role. If the outer layer is very thin compared to its curvature, an object's surface will likely be convoluted, similar to a fingerprint. If the shell is a bit thicker, the surface will form a more hexagonal pattern.

The group's theory, although primarily based on work with spheres, may also apply to more complex objects and the theory could serve as a design tool to engineer objects with morphable surfaces.

Justin Cunningham

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