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The mechanical properties of folded maps

Folding Miura-ori patterns. Courtesy of MetaNest on Wikimedia Commons.

Folding Miura-ori patterns. Courtesy of MetaNest on Wikimedia Commons.

The origami trick now often used to fold large maps into small rectangles was developed by Japanese aerospace scientist Koryo Miura at the University of Tokyo, who originally invented it to help deploy solar panels on spacecraft. Now researchers find that materials possessing these Miura-ori folds possess intriguing mechanical properties.

First structural engineers modeled a single Miura sheet that is partly folded, giving it a corrugated appearance. They considered deforming it two possible ways—either out-of-plane, meaning bending it three-dimensionally, or in-plane, meaning squeezing or stretching its edges straight toward or away from its center.

When bent out-of-plane, this sheet responded fairly normally—when compressed along one axis, it expands along the other two perpendicular axes. (Think of how a jelly doughnut squirts outward when squeezed.) This phenomenon is what you expect of a material with what is called a positive Poisson’s ratio.

However, when deformed in-plane, this sheet behaved the opposite way—when stretched along one axis, they actually expand along the other two perpendicular axes. (Think of how an accordion’s bellows puff out when you pull at them.) This means it is also auxetic, or has a negative Poisson’s ratio.

“We’re looking at how you can change the properties of a structure not by using a clever new material, but by using standard materials with some texturing on its surface,” said researcher Simon Guest at the University of Cambridge in England.

The researchers also stacked partly folded Miura sheets together to make three-dimensional structures. The result was a material that could fold and unfold uniformly.

“We’re interested in developing metamaterials—materials where you deliberately build micro-structures into them—and it would be interesting to see if metamaterials based on Miura sheets could work on a large scale, with whole buildings that could collapse down or fold up for use as deployable buildings, for instance,” Guest said.

Applications for stacked Miura layers may also include impact-absorbing materials. “You can imagine building armor that can protect from blasts, or energy-absorbing structures in an automobile,” Guest said.

Guest and his colleague Mark Schenk detailed their findings online Feb. 11 in the Proceedings of the National Academy of Sciences.

Categories: Applied Physical Sciences
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