Take a piece of paper. Fold it in half, and you’ve turned a floppy sheet into a three-dimensional structure that can stand up, even if a bit wobbly, on its own.
A few more deliberate folds, and you may even have an airplane capable of actual flight. Or, with a little more patience, a crane, a rhinoceros, or almost any object, shape, or design you can imagine.
From this simple act of folding, you can create enormous complexity—something origami artists have been doing for hundreds of years, transforming paper into art. But recently, that art has also become useful, as origami has begun to merge with engineering. Origami principles have inspired novel ways of packaging airbags, fashioning heart stents, folding solar sails designed to propel spacecraft, and even collapsible bullet-proof shields.
And researchers are just getting started. They’re now using origami to design materials of the future: materials that shift from soft to stiff—and back again—with the flick of a switch, or smart materials that respond to their environments as if they were alive. Combined with robotics and devices, these materials may redefine what it even means to be a material, with potential applications in engineering, architecture, biology, medicine, and beyond.
A lot of modern research in origami engineering traces back to an astrophysicist named Koryo Miura who, in 1970, came up with simple but elegant fold. It consists of creases that form a pattern of tiled parallelograms, allowing it to collapse and open with ease. Known as the Miura fold, or Miura-ori, he later repurposed the fold as a way to package large, flat membranes for deploying into space. In fact, in 1995, a Japanese satellite used the fold to store its solar panels for launch and unfurl them once in orbit.
In the years since, the Miura-ori has become one of the most well-studied folds, prompting Cornell engineer Itai Cohen to call it the hydrogen atom of origami. Like hydrogen, the pattern is simple, yet imbued with complex and exotic properties. When you squeeze a Miura-ori on its sides, for example, the top and bottom also collapses inward. This feature, known as a negative Poisson ratio, is unusual. Most other things spill outward in the direction perpendicular to your squeezing. Hold a sandwich too tight, and your meat and fixins’ will squirt out the sides.
You can also adjust the stiffness of the fold. Cohen and his colleagues have shown how defects—forcing certain creases to fold in the opposite way—can make the Miura-ori rigid. “You can just take the same fold pattern and poke it in certain places and suddenly it responds differently than if you poke it in different places,” says Christian Santangelo of the University of Massachusetts, Amherst. In this sense, Miura-ori represents a switchable material whose properties—stiffness, in this case—can be toggled and tuned on the fly.
Something folded into a Miura-ori is an example of a metamaterial, a material whose properties depend not on what it’s made of, but on its structure. Maybe the most famous example is an invisibility cloak, a material embedded with nanoscale structures that can redirect light around an object, making it appear invisible.
But unlike conventional metamaterials, whose properties are built-in, foldable structures introduce a powerful new dynamic: the ability to transform. “We can in principle dial in any mechanical properties you want,” Santangelo says. “By changing the structure, you can have something that’s very soft or very hard. Or, it starts out being very soft and gets hard.”
Using a building-block approach, Johannes Overvelde at AMOLF, a research institute in the Netherlands, Katia Bertoldi at Harvard, and others, have developed a different way of achieving complex structures. By stacking identical 3D cube-like structures together, the researchers can build a larger structure that, through folding, morphs into different shapes and configurations.
In this modular strategy, dubbed snapology, the properties of each building block can generally transfer to the whole structure. “If you start from all rigid unit cells, your metamaterial becomes rigid as well,” Overvelde says. “If unit cells are more foldable, then potentially the metamaterial is more foldable and more configurable.”
In a proof-of-concept example, he and his colleagues used snapology to build a network of plastic tubes that channel sound waves. They can reconfigure the structure by hand or with air pressure, changing and controlling how the sound travels. Someday, Overvelde says, an acoustic waveguide like this may be embedded into the ceiling of a room or concert hall, reconfiguring itself to dampen noise or change how sound travels.
But that’s just one design. The possibilities, he says, are nearly endless. The researchers have devised a systematic strategy to produce tens of thousands of reconfigurable shapes and structures based on snapology. In principle, an engineer could search through this database, hunting for designs with the right properties needed for a particular application.
For now, though, Overvelde has just explored what’s possible with various geometries and designs, making prototypes out of cardboard. But if the three-dimensional structures he envisions are ever going to be useful, engineers will have to fabricate them out of more durable materials—likely in a range of size scales–which isn’t a trivial matter. One solution is 3D printing, but the technology isn’t yet up to snuff.
This is where folding 3D structures from 2D sheets, like Miura-ori, has an advantage. After all, the power of origami lies in the fact that it’s easier to fold a structure than to build it from the ground up, which is generally how conventional metamaterials are made. From laser cutting to lithographic techniques that can etch nanoscale features on chips, 2D-printing methods are more advanced and faster than 3D printing. “We can print anything we want, really, in 2D,” says Erik Demaine, an origami artist and computer scientist at MIT.
A Universal Algorithm
What might make it even easier is software that makes designs for you. Software such as TreeMaker, created by origami artist and physicist Robert Lang, or Origamizer, by Tomohiro Tachi of the University of Tokyo, can determine crease patterns for different shapes, helping origami artists create increasingly sophisticated designs.
Although powerful, the software can’t turn every shape into origami. So Tachi and Demaine set out to develop a universal algorithm that can find a crease pattern for any 3D surface. After a decade of work, they’ve now succeeded and presented their algorithm in July of last year. Once they encode their algorithm into the next version of Origamizer, you’ll be able to input a 3D rendering of your face, the Manhattan skyline, or any other surface, and the software will spit out a corresponding crease pattern.
Even the algorithm has its limits, however. It assumes you have an infinitely thin sheet of material. Paper is thin, but not that thin, so adapting to real-world origami may be a little tricky. The algorithm is optimized to give you a set of folds that most efficiently uses a sheet of paper. But for metamaterials, that’s not necessarily what you want.
“Origamizer is all about folding your material into the right shape,” Demaine says. “But in reality, and especially in metamaterials, you also care about structural properties.” The new algorithm doesn’t yet allow you to make designs based on structural properties, but future incarnations might, he says. Still, the new-and-improved Origamizer marks a significant achievement and can help design metamaterials.
The Amazing Self-Folding Microbot
But design is just the start. The key to origami is, of course, folding. And a major goal among researchers is to develop a way for structures to fold by themselves. Switchable and reconfigurable metamaterials won’t be very useful if you have to fold it by hand—and they’ll be nearly impossible to manage if they require microscopic folds.
Most strategies use materials that shrink or expand at different rates in response to heat, for example. If you layer the materials together and apply heat, only one of the materials will contract, forcing the entire sheet to buckle. By designing your sheet to buckle only along designated creases, you can get it to fold up into whatever pattern you want.
Finding the right shrinking or expanding materials isn’t easy, however. Researchers like Santangelo, for example, have experimented with hydrogels, which swell in water. “The problem with hydrogels is that they’re very slow and weak,” he says. “They’re great for proving proofs-of-principle—not so great when you have to do actual physical work.”
But now Cohen thinks he has an answer. Working with Marc Miskin at Cornell, Cohen has found a way to get strong, rigid panels to fold in less than a second. These structures are also tiny—about the size of a biological cell—which would make them potentially useful for medicine: imagine sending tiny, self-folding robots into the body to attack a virus or a tumor. “It’s the first real platform for the kind of nanotechnology you see in science fiction,” Miskin says.
The panels bend along hinges just two nanometers thick that are made of glass stuck to a single sheet of graphene, an atom-thin layer of carbon that’s as stiff and, at the atomic scale, stronger than diamond. To get it to fold, the researchers dip the material into a chemical bath and increase its acidity. A higher acidity drives larger ions to replace smaller ones in the glass, which forces the glass to expand—and the sheet to bend. A more basic solution reverses the process.
Again, the big draw for a self-folding device is that it fits seamlessly into current 2D lithographic and semiconductor technology, making manufacturing easier, Cohen says. The fact that these devices fold up also means you can squeeze them into compact spaces. The self-folding action can even do physical work, such as propulsion through the body or exerting force on a cell.
The researchers have built a prototype that folds into a 15-micron-wide tetrahedron, just three times bigger than a red blood cell. As proofs-of-principle, they’ve built small helices, cubes, a Miura-ori unit, and a book that clasps shut. “This ends up being a blank slate you can now design real machines for,” Cohen says. “Now the question is what you should put on there to make the machine you want.”
Future robots, he says, could measure the properties of cells, interact with them, or trigger cellular responses. Because graphene is electrically conductive, you can attach electronic sensors or other components. For example, the researchers are exploring how to incorporate light sensors, which could be useful for biomedical research. Because their self-folding devices are sensitive to ions, they also envision using them to gauge ion concentrations in the body—and in doing so, maybe even measure when neurons are firing in the brain.
Material or Machine?
Indeed, integrating devices into self-folding structures may be the materials of the future. Overvelde, for example, is now trying to embed sensors into his 3D reconfigurable structures. He hopes to design smart metamaterials that sense their environments and reconfigure themselves in response—a kind of emergent behavior akin to flocking birds or schools of fish. Because the response doesn’t depend on a central computer or device, the structure will still work even if sliced in half.
This kind of technology may bring to mind T-1000, the shape-shifting homicidal robot from the movie Terminator 2, or the green blob from Flubber. “That’s clearly science fiction at the moment,” says Martin van Hecke of AMOLF. But as devices become more integrated with materials, the boundary between the two will blur. “If you really think ahead of what we’ll have in 50 years, I would expect that some devices we wouldn’t even recognize as devices. They might look like a piece of Jell-O or inert plastic, and they would pop into something completely different. I don’t see a physical reason why that’s impossible.”
As even today’s origami-inspired structures are showing, there’s less distinction between material and machine. “To me personally, that’s an exciting thing because it means, conceptually, a different type of object,” he says.
That amalgamation of material and machine may even include Cohen’s cell-sized self-folding robots. He imagines linking them together, creating an interconnected swarm that behaves more like a material, comparable to the microbots in the movie Big Hero 6.
But as of now, their technology—and other origami-inspired metamaterial-slash-robot—is just an important proof-of-principle, Cohen says. “The rest of this is our vision,” he says. “The chance that it all comes true is zero. The chances that some comes true, or at least inspires something that does come true, are quite high.”