Inspired by bones and other cellular solids found in nature, humans have used the same concept to develop architected materials. By changing the geometry of the unit cells that make up these materials, researchers can customize the material’s mechanical, thermal, or acoustic properties. Architected materials are used in many applications, from shock-absorbing packing foam to heat-regulating radiators.

Using kirigami, the ancient Japanese art of folding and cutting paper, MIT researchers have now manufactured a type of high-performance architected material known as a plate lattice, on a much larger scale than scientists have previously been able to achieve by additive fabrication. This technique allows them to create these structures from metal or other materials with custom shapes and specifically tailored mechanical properties.

“This material is like steel cork. It is lighter than cork, but with high strength and high stiffness,” says Professor Neil Gershenfeld, who leads the Center for Bits and Atoms (CBA) at MIT and is senior author of a new paper on this approach.

The researchers developed a modular construction process in which many smaller components are formed, folded, and assembled into 3D shapes. Using this method, they fabricated ultralight and ultrastrong structures and robots that, under a specified load, can morph and hold their shape.

Because these structures are lightweight but strong, stiff, and relatively easy to mass-produce at larger scales, they could be especially useful in architectural, airplane, automotive, or aerospace components.

Joining Gershenfeld on the paper are co-lead authors Alfonso Parra Rubio, a research assistant in the CBA, and Klara Mundilova, an MIT electrical engineering and computer science graduate student; along with David Preiss, a graduate student in the CBA; and Erik D. Demaine, an MIT professor of computer science. The research will be presented at ASME’s Computers and Information in Engineering Conference.

Fabricating by folding

Architected materials, like lattices, are often used as cores for a type of composite material known as a sandwich structure. To envision a sandwich structure, think of an airplane wing, where a series of intersecting, diagonal beams form a lattice core that is sandwiched between a top and bottom panel. This truss lattice has high stiffness and strength, yet is very lightweight.

Plate lattices are cellular structures made from three-dimensional intersections of plates, rather than beams. These high-performance structures are even stronger and stiffer than truss lattices, but their complex shape makes them challenging to fabricate using common techniques like 3D printing, especially for large-scale engineering applications.

The MIT researchers overcame these manufacturing challenges using kirigami, a technique for making 3D shapes by folding and cutting paper that traces its history to Japanese artists in the 7th century.

Kirigami has been used to produce plate lattices from partially folded zigzag creases. But to make a sandwich structure, one must attach flat plates to the top and bottom of this corrugated core onto the narrow points formed by the zigzag creases. This often requires strong adhesives or welding techniques that can make assembly slow, costly, and challenging to scale.

The MIT researchers modified a common origami crease pattern, known as a Miura-ori pattern, so the sharp points of the corrugated structure are transformed into facets. The facets, like those on a diamond, provide flat surfaces to which the plates can be attached more easily, with bolts or rivets.

“Plate lattices outperform beam lattices in strength and stiffness while maintaining the same weight and internal structure,” says Parra Rubio. “Reaching the H-S upper bound for theoretical stiffness and strength has been demonstrated through nanoscale production using two-photon lithography. Plate lattices construction has been so difficult that there has been little research on the macro scale. We think folding is a path to easier utilization of this type of plate structure made from metals.”

Customizable properties

Moreover, the way the researchers design, fold, and cut the pattern enables them to tune certain mechanical properties, such as stiffness, strength, and flexural modulus (the tendency of a material to resist bending). They encode this information, as well as the 3D shape, into a creasing map that is used to create these kirigami corrugations.

For instance, based on the way the folds are designed, some cells can be shaped so they hold their shape when compressed while others can be modified so they bend. In this way, the researchers can precisely control how different areas of the structure will deform when compressed.

Because the flexibility of the structure can be controlled, these corrugations could be used in robots or other dynamic applications with parts that move, twist, and bend.

To craft larger structures like robots, the researchers introduced a modular assembly process. They mass produce smaller crease patterns and assemble them into ultralight and ultrastrong 3D structures. Smaller structures have fewer creases, which simplifies the manufacturing process.

Using the adapted Miura-ori pattern, the researchers create a crease pattern that will yield their desired shape and structural properties. Then they utilize a unique machine — a Zund cutting table — to score a flat, metal panel that they fold into the 3D shape.

“To make things like cars and airplanes, a huge investment goes into tooling. This manufacturing process is without tooling, like 3D printing. But unlike 3D printing, our process can set the limit for record material properties,” Gershenfeld says.

Using their method, they produced aluminum structures with a compression strength of more than 62 kilonewtons, but a weight of only 90 kilograms per square meter. (Cork weighs about 100 kilograms per square meter.) Their structures were so strong they could withstand three times as much force as a typical aluminum corrugation.

The versatile technique could be used for many materials, such as steel and composites, making it well-suited for the production lightweight, shock-absorbing components for airplanes, automobiles, or spacecraft.

However, the researchers found that their method can be difficult to model. So, in the future, they plan to develop user-friendly CAD design tools for these kirigami plate lattice structures. In addition, they want to explore methods to reduce the computational costs of simulating a design that yields desired properties.

Parra Rubio, Mundilova and other MIT graduate students also used this technique to create three large-scale, folded artworks from aluminum composite that are on display at the MIT Media Lab. Despite the fact that each artwork is several meters in length, the structures only took a few hours to fabricate.

“At the end of the day, the artistic piece is only possible because of the math and engineering contributions we are showing in our papers. But we don’t want to ignore the aesthetic power of our work,” Parra Rubio says.

This work was funded, in part, by the Center for Bits and Atoms Research Consortia, an AAUW International Fellowship, and a GWI Fay Weber Grant.

“The chemical industry is a massive energy consumer, and there is a big push to decarbonize the industry,” says Shannon Stahl, a professor in the UW-Madison Department of Chemistry who guided much of the research. “Renewable electricity can provide energy to produce chemicals with a much lower carbon footprint than burning fossil fuels.”

The conventional process uses large quantities of zinc metal as the source of electrons, but handling zinc is complicated and generates large amounts of environmentally unfriendly waste. Working with scientists at the pharmaceutical maker Merck & Co. Inc., UW-Madison chemists and engineers sought to develop a more sustainable method to manufacture ingredients needed to make many types of drugs.

In their search for an alternative process, the researchers took inspiration from hydrogen fuel cells, which use hydrogen gas as the source of electrons to generate electricity.

“The process we are working with needs a green source of electrons,” says Stahl. “We realized that fuel cell technology could be modified to make chemicals rather than electricity,”

Hydrogen gas is an ideal choice in many ways, according to Stahl. It can be generated from renewable electricity, and it creates very little waste. Developing a hydrogen-based way to make pharmaceuticals aligns with renewed interest in a “hydrogen economy.”

“This work is connected to a broader effort to create a hydrogen infrastructure that goes beyond fuel cells and energy production,” says Mathew Johnson, a postdoctoral researcher in the chemistry department who led the study. “This work shows that hydrogen can be combined with electricity to make new drugs.”

The researchers developed a system that uses a type of organic compound called a quinone to pull electrons away from hydrogen. An important feature of this process is that it works well in the absence of water. Fuel cells typically need water to operate effectively, but water can interfere with steps used to make the drug ingredients.

The system then uses electricity to supercharge the electrons, giving the electrons more energy than hydrogen could normally provide.

The team, which included postdoctoral researcher Jack Twilton, chemistry professor Daniel Weix and chemical and biological engineering professor Thatcher Root, described their new system in a paper published Aug. 21 in the journal Nature[1] . They show how it can be used to make dozens of important organic molecules, including a large batch of a pharmaceutical ingredient.

The team is now working to improve the process so it can be used for industrial-scale production. And Stahl and his collaborators see even bigger opportunities for this technology.

“This is a broadly applicable technology for chemical production,” says Johnson. “Many chemical processes need electrons. This is not limited to pharmaceuticals. It should be a very versatile technology.”

The work, led by Xiaofeng Qian, assistant professor of physics at Stevens and reported in the August 17 online issueof Physical Review Research, also proves for the first time that a light wave’s degree of non-quantum entanglement exists in a direct and complementary relationship with its degree of polarization. As one rises, the other falls, enabling the level of entanglement to be inferred directly from the level of polarization, and vice versa. This means that hard-to-measure optical properties such as amplitudes, phases and correlations — perhaps even these of quantum wave systems — can be deduced from something a lot easier to measure: light intensity.

“We’ve known for over a century that light sometimes behaves like a wave, and sometimes like a particle, but reconciling those two frameworks has proven extremely difficult,” said Qian “Our work doesn’t solve that problem — but it does show that there are profound connections between wave and particle concepts not just at the quantum level, but at the level of classical light-waves and point-mass systems.”

Qian’s team used a mechanical theorem, originally developed by Huygens in a 1673 book on pendulums, that explains how the energy required to rotate an object varies depending on the object’s mass and the axis around which it turns. “This is a well-established mechanical theorem that explains the workings of physical systems like clocks or prosthetic limbs,” Qian explained. “But we were able to show that it can offer new insights into how light works, too.”

This 350-year-old theorem describes relationships between masses and their rotational momentum, so how could it be applied to light where there is no mass to measure? Qian’s team interpreted the intensity of a light as the equivalent of a physical object’s mass, then mapped those measurements onto a coordinate system that could be interpreted using Huygens’ mechanical theorem. “Essentially, we found a way to translate an optical system so we could visualize it as a mechanical system, then describe it using well-established physical equations,” explained Qian.

Once the team visualized a light wave as part of a mechanical system, new connections between the wave’s properties immediately became apparent — including the fact that entanglement and polarization stood in a clear relationship with one another.

“This was something that hadn’t been shown before, but that becomes very clear once you map light’s properties onto a mechanical system,” said Qian. “What was once abstract becomes concrete: using mechanical equations, you can literally measure the distance between ‘center of mass’ and other mechanical points to show how different properties of light relate to one another.”

Clarifying these relationships could have important practical implications, allowing subtle and hard-to-measure properties of optical systems — or even quantum systems — to be deduced from simpler and more robust measurements of light intensity, Qian explained. More speculatively, the team’s findings suggest the possibility of using mechanical systems to simulate and better-understand the strange and complex behaviors of quantum wave systems.

“That still lies ahead of us, but with this first study we’ve shown clearly that by applying mechanical concepts, it’s possible to understand optical systems in an entirely new way,” Qian said. “Ultimately, this research is helping to simplify the way we understand the world, by allowing us to recognize the intrinsic underlying connections between apparently unrelated physical laws.”

Modern cats belong to one of two groups: either the pantherine “big cats,” including the roaring lions, tigers and jaguars; or Felinae “little cats,” which include purring cats like lynxes, cougars, ocelots and domestic cats.

“Evolutionarily speaking, sabertooths split off the cat family tree before these other modern groups did,” says Adam Hartstone-Rose, professor of biological sciences at NC State and corresponding author of the research. “This means that lions are more closely related to housecats than either are to sabertooths.

“That’s important because the debate over the kind of vocalization a sabertooth tiger would have made relies upon analyzing the anatomy of a handful of tiny bones located in the throat,” Hartstone-Rose says. “And the size, shape and number of those bones differ between modern roaring and purring cats.”

Although vocalization is driven by the larynx and soft tissue in the throat, not bones, anatomists noticed that the bones responsible for anchoring those tissues in place — the hyoid bones — differed in size and number between roaring and purring cats.

“While humans have only one hyoid bone, purring cats have nine bones linked together in a chain and roaring cats have seven,” says Ashley Deutsch, a Ph.D. student at NC State and lead author of the research. “The missing bones are located toward the top of the hyoid structure near where it connects to the skull.”

“Because sabertooth tigers only have seven bones in their hyoid structure, the argument has been that of course they roared,” Hartstone-Rose says. “But when we looked at the anatomy of modern cats, we realized that there isn’t really hard evidence to support this idea, since the bones themselves aren’t responsible for the vocalization. That relationship between the number of bones and the sound produced hasn’t ever really been proven.”

The researchers looked at the hyoid structures of four species of roaring cats: lions, tigers, leopards and jaguars; and five species of purring cats: cougars, cheetahs, caracals, servals and ocelots. They compared these to 105 hyoid bones from the iconic sabertooth tiger Smilodon fatalis.

“You can argue that since the sabertooths only have seven bones they roared, but that’s not the whole story,” Hartstone-Rose says. “The anatomy is weird. They’re missing extra bones that purring cats have, but the shape and size of the hyoid bones are distinct. Some of them are shaped more like those of purring cats, but much bigger.”

According to the researchers, if the missing bones (called epihyoid bones) were key to different vocalizations, the bones most closely connected to them should look different between the two groups. However, those bones looked very similar in shape whether they came from purring or roaring cats.

In fact, the researchers saw more shape variation in the bones closer to the vocal apparatus; i.e., the thyrohyoid and basihyoid bones. The uniformity of the upper bones between the two groups suggests that if the hyoid structure plays a role in vocalization, the lower bones are more important than the upper ones. So having these key hyoid bones shaped like those of purring cats could indicate that they purred rather than roared.

“We found that despite what history has told us about the number of bones in the hyoid structure, no one has validated the significance of that difference,” Hartstone-Rose says. “If vocalization is about the number of bones in the hyoid structure, then sabertooths roared. If it’s about shape, they might have purred. Due to the fact that the sabertooths have things in common with both groups, there could even be a completely different vocalization.”

“It is perhaps most likely that the size of the hyoids plays a role in the pitch of vocalization,” says Deutsch. “Although Smilodon wasn’t quite as big as the largest modern cats, its hyoid bones are substantially larger than those of any of their living relatives, so potentially they had even deeper vocalizations than the largest tigers and lions.”

The work appears in the Journal of Morphology and was supported by NC State’s Office of Undergraduate Research. Brian Langerhans, associate professor of biology at NC State, and former NC State undergraduate Deanna Flores also contributed to the work.