Scientists lay out why some origami won't fold under pressure

January 4, 2018 by Louise Lerner, University of Chicago

Scientists and engineers are fascinated by self-folding structures. Imagine the possibilities: heart stents that unfold in the right location or pop-up tents that assemble at the press of a button, as well as nanoscale versions for tiny machines. But sometimes these structures get stuck during the folding process, and scientists don't know why.

A new paper in Physical Review X by three University of Chicago scientists lays out a mathematical explanation—such sticking points are simply intrinsic.

"People thought you could engineer around it, but it really looks like there are fundamental limits," said graduate student Menachem Stern, the first author on the paper.

Structures designed to self-assemble often start out correctly, but then the folding peters out, leaving behind islands of properly folded parts. To explore why, the team created a set of mathematical models.

When designing structures that can fold themselves, whether paper or tiny nanomachines, scientists start by pre-creasing the folds they need. But this also creates a set of invisible "distractor" branches. The more pre-creases added, the more distractor branches form, and the origami is more and more likely to get stuck.

"No matter how clever the design, there are always many more ways to fold incorrectly and get stuck than to fold correctly," said Arvind Murugan, assistant professor in the James Franck Institute and coauthor on the paper. "We realized that this problem of having many more ways to do something incorrectly than correctly shows up in many other areas of science and mathematics, including the design of protein structures in biology and the design of Sudoku puzzles."

Credit: University of Chicago

Using these connections, there are ways to mitigate the problem even if it is intrinsic, said Stern, Murugan and Matthew Pinson, the study's third author.

Their findings include a set of predictions for where to place hinges when designing folds, as well as for identifying problem areas and how to fix them—which could apply to everything from origami to micro-machines to self-assembling tents.

Explore further: 'Origami' lattices with nano-scale surface ornaments

More information: Menachem Stern et al. The Complexity of Folding Self-Folding Origami, Physical Review X (2017). DOI: 10.1103/PhysRevX.7.041070

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not rated yet Jan 04, 2018
Could also explain why several solar sail designs have snarled...
Thorium Boy
2 / 5 (2) Jan 04, 2018
What is this weird fixation with this Asian paper artwork? I've seen three stories about origami in scientific sites in the last few months.
not rated yet Jan 05, 2018
TB, a few reasons why this fixation:

Solar sails, as Nik points out, have often been built along origame designs for launch, and then do not quite unfold right afterwards. Also it has applications towards cheap space construction and insulation.

Getting to understand proteins, which also do strange self-folding and have some similar properties to origame, some models have been based on this approach and works for certain protein bases and medical research, items and devices (stents and other structures).

Robotics and areas such as armor proofing have found uses for origame in either construction or structural usage of precision folding and even todays aircraft, like Airbus and Boeing Dreamliner, are basically folded carbon-carbon cloth carefully folded together and bonded in massive autoclaves, then mated with hulls made same basic way.

So there really are a lot of modern applications for what seemed like an ancient, not so simple, basic pastime.

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