Design Engineering

New computational design tool turns flat sheets into complex 3D shapes



Researchers make hexagonal cuts into flexible but not normally stretchable plastic and metal sheets to give them the ability to expand uniformly.

Turning flat sheets of plastic or metal into complex 3D shapes is now easier than ever.

computational design tool 3D printing

A computational design tool created a pattern of perforations that enabled a flat sheet of copper to form a 3-D mask. This tool could be used to explore the possibilities of materials that stretch uniformly. Photo courtesy of David J. Srolovitz,

Researchers at Carnegie Mellon University and the Swiss Federal Institute of Technology in Lausanne, Switzerland (EPFL), have created a new computational design tool that allows designers to harness the unusual quality of certain materials, uniformly expanding in two dimensions. The team was able to make hexagonal cuts into flexible, but not normally stretchable plastic and metal sheets to give them the ability to expand uniformly up to a certain point.

The team believes the design tool could be used for a variety of auxetic materials, which share this distinctive quality. This advancement could have several unique applications in biomechanics, consumer goods and architecture, said Mark Pauly, professor of computer and communications sciences at EPFL.

“We’re taking a flat piece of material and giving it the tendency, or even the desire, to bend into a certain 3D shape,” said Keenan Crane, assistant professor of computer science and robotics at Carnegie Mellon.


Through this design tool, auxetic materials will be able to approximate double-curved surfaces, such as spheres, using only flat pieces.

“Artists and designers have played around with these materials, but ultimately they have been limited by the things they could fashion by hand,” Crane said. “We wanted to see what you could do if you got computation involved.”

Metal and plastic sheets, altered with cuts to lend them auxetic qualities, are convenient materials to explore how to create these complex designs, Crane said.

In this study, a series of hexagonal slits were cut into the sheets to create triangular elements that were able to rotate relative to their neighbors, allowing them to expand uniformly.

The new computational tool will help designers determine the pattern of slits needed to make the sheet conform to the correct shape. 


Researchers used a new computational design tool to make this high-heel shoe. The base of the shoe was 3-D printed, and the upper part was fashioned from auxetic material.



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