New mathematical theory explains how wrinkles can be predicted

NewMathsTheory 0302Washington (ISJ): Ever wondered how wrinkles are formed! A mathematical theory based on experiments rightly predicts how wrinkles on curved surfaces take shape.

A team of mathematicians and engineers from the Massachusetts Institute of Technology (MIT) has developed a theory which may help explain how fingerprints and wrinkles form.

"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 J�rn Dunkel, an 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," he added.

The researchers say the more curved a surface is, the more its surface patterns resemble a crystal-like lattice.

The group sought to develop a general theory to describe how wrinkles on curved objects form ? a goal that was initially inspired by observations made by Dunkel's collaborator, Pedro Reis, the Gilbert W. Winslow Career Development Associate Professor in Civil Engineering.

The researchers carried out computer simulations which confirmed that their equation was able to reproduce correctly the surface patterns observed in experiments.

It helped them identifying the main parameters that govern surface patterning. Curvature was found to be a major factor in determining whether a wrinkling surface becomes covered in hexagons or a more labyrinthine pattern. 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.

Source: MIT

Image courtesy: MIT

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