Editors' notes
Research led at the University of Michigan modeled how different origami structures made from trapezoidal subunits (i) responded to stresses like compression (ii) and stretching (iii). Credit: Nature Communications (2025). DOI: 10.1038/s41467-025-57089-x
Origami—the art of paper folding that originated in Japan centuries ago—could open a new frontier in innovative materials, thanks to research led at the University of Michigan.
The research is published in the journal Nature Communications.
As an art, origami uses simple folding techniques to create intricate designs. Now, researchers are studying the technique as the foundation for next-generation materials that predictably deform and "fold" under the right forces. Such materials would be useful in a wide variety of applications, including running shoes, heart stents and airplane wings.
"Origami has received a lot of attention over the past decade due to its ability to deploy or transform structures," said James McInerney, lead author of the new study who performed the work as a postdoctoral fellow at the University of Michigan. McInerney is now a National Research Council research associate at the Air Force Research Laboratory.
"Our team wondered how different types of folds could be used to control how a material deforms when different forces and pressures are applied to it."
McInerney and colleagues have introduced a new way of modeling folds to better understand how they can control a material's properties, which is a deceptively complicated problem.
In principle, the idea is akin to how a creased piece of cardboard folds more predictably than a pristine piece that could buckle in any number of ways under pressure. By introducing folds, then, the researchers can tune how materials respond to force. The applications of that type of control are vast, McInerney said.
"There are a variety of scenarios ranging from the design of buildings, aircraft and naval vessels to the packaging and shipping of goods where there tends to be a trade-off between enhancing the load-bearing capabilities and increasing the total weight," McInerney said. "Our end goal is to enhance load-bearing designs by adding origami-inspired creases—without adding weight."
The study also includes Zeb Rocklin, McInerney's doctoral adviser at the Georgia Institute of Technology; Xiaoming Mao, professor of physics at the University of Michigan; Glaucio Paulino of Princeton University; and Diego Misseroni of the University of Trento.
"Broadly speaking, this origami is an example of 'metamaterials'—engineered materials where novel properties are achieved through programming the structure instead of the chemical ingredients," Mao said. "The geometry of folding—simple to achieve in practice—endows a piece of paper with completely new properties."
Below the fold
Although flat materials, like pieces of paper, are easy enough to conceptualize, their behaviors under force are complex.
"If I tug on either end of a sheet of paper, it's solid—it doesn't separate," said Rocklin, associate professor of physics at Georgia Tech. "But it's also flexible. It can crumple and wave depending on how I move it. That's a very different behavior than what we might see in a conventional solid, and a very useful one."
Introducing creases can "program" the materials to behave a certain way, but determining how and when to make those folds is a challenge, even for modern physics.
"With these materials, it is often difficult to predict what is going to happen—how the material will deform under pressure, because they can deform in many different ways," Rocklin said.
"Conventional physics techniques can't solve this type of problem, which is why we're still coming up with new ways to characterize structures in the 21st century."
When considering origami-inspired materials, physicists start with a flat sheet that's carefully creased to create a specific three-dimensional shape. But the method is limited. Researchers have previously only modeled parallelogram-based folding, which uses shapes like squares and rectangles, allowing for limited types of deformation.
So Rocklin, McInerney and their colleagues turned to trapezoids, which have just one set of parallel sides. Introducing these more variable shapes makes this type of creasing more difficult to model, but more versatile.
"From our models and physical tests, we found that trapezoid faces have an entirely different class of responses," McInerney said. And those responses lead to new functionality, he added.
The designs had the ability to change their shape in two distinct ways: "breathing" by expanding and contracting evenly, and "shearing" by deforming in a twisting motion.
Surprisingly, the team also found that some of the behavior in parallelogram-based origami carried over to their trapezoidal origami, hinting at some features that might be universal across designs.
"While our research is theoretical, these insights could give us more opportunities for how we might deploy these structures and use them," Rocklin said.
"It's a very challenging problem, but biology and nature are full of smart solids—including our own bodies—that deform in specific, useful ways when needed. That's what we're trying to replicate with origami."
More information: James P. McInerney et al, Coarse-grained fundamental forms for characterizing isometries of trapezoid-based origami metamaterials, Nature Communications (2025). DOI: 10.1038/s41467-025-57089-x
Provided by University of Michigan
