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What Are the Physics of Origami and Kirigami?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

Origami is the art of folding paper to make structures, which can be stated more rigorously as taking a 2D material and applying transformations to it without changing its manifold until we arrive at a 3D object. The discipline of origami doesn’t have a definite origination date but is stemmed deeply into Japanese culture. However, it can often be dismissed as a casual

Miura-ori Patterns

One of the first patterns from origami used in a scientific application was the Miura-ori pattern. Developed in 1970 by astrophysicist Koryo Miura, it is a “tessellation of parallelograms” that compacts in a nice fashion that is both efficient and aesthetically pleasing. Miura developed the pattern because he was tossing around the idea that his pattern could be used in solar panel technology and in 1995 it was, aboard the Space Flyer Unit. The ability to fold naturally would save space on a rocket launch, and if the probe were to return to Earth it would allow for successful recovery. But another inspiration was nature. Miura saw patterns in nature like wings and geological features which didn’t involve nice right angles but instead seem to have tessellations. It was this observation that eventually led to the discovery of the pattern, and applications for the material seem boundless. Work from the Mahadevan Lab shows that the pattern can be applied to many different 3D shapes using a computer algorithm. This could allow material scientists to customize equipment with this and make it incredibly portable (Horan, Nishiyama, Burrows).



Miura-ori Deformed

So the Miura-ori pattern works because of its tessellation properties, but what if we purposefully caused an error in the pattern, then introduce statistical mechanics? That’s what Michael Assis, a physicist at the University of Newcastle in Australia, sought to uncover. Traditionally, statistical mechanics is used for gather emergent details on systems of particles, so how can that be applied to origami? By applying the same ideas to the central concept of origami: the folding. That is what falls under analysis. And one easy way to change a Miura-ori pattern is to push in a segment so that it becomes a compliment shape, i.e. convex if concave and vice versa. This could happen if one is vigorous with the folding and releasing process. In nature, this reflects deformities in a crystal pattern as it is heated up, increasing energy and causing deformities to form. And as the process goes on, those deformities eventually even out. But what was surprising was the Miura-ori seemed to undergo a phase transition – much like matter! Is this a result of chaos forming in the origami? It should be noted that Barreto’s Mars, another tessellating origami pattern, does not undergo this change. Also, this origami run was a simulation and doesn’t take into account the minute imperfections that real origami has, possibly inhibiting the results (Horan).


Kirigami is similar to origami but here we can not only fold but also make cuts into our material as needed, and so because of its similar nature I’ve included it here. Scientists see many applications for this, as is often the case with a mathematically beautiful idea. One of those is efficiency, especially with the folding of the material for easy shipment and deployment. For Zhong Lin Wang, a materials scientist from Georgia Institute of Technology in Atlanta, the ability to use kirigami for nanostructures is the goal. Specifically, the team is looking for a way to make a nanogenerator which exploits the triboelectric effect, or when moving physically causes electricity to flow. For their design, the team used a thin copper sheet between two pieces of also thin paper which has some flaps on it. It is the movement of these which generates a small amount of juice. Very small, but enough to power some medical devices and possible be a power source for nanobots, once the design is scaled down (Yiu).

Kirigami Metamaterials

Using kirigami principles, Zhang Hongying (National University of Singapore) and Jamie Palk (Swiss Federal Institute of Technology in Lausanne) were able to make a cubic metamaterial with a side length of 5 centimeters and a mass of 12 grams which could support a 35 kilogram weight. For those doing the number crunching, that means one of these cubes could hold up a tower of these nearly 2917 times its original height! The kirigami used involved interlocking squares which are ten capable of being manipulated into various 3D shapes, the cube just being one of them. Such a material would be of great interest in many industries, so now a mass-production means of manufacturing these needs to be found (Wilkins).

DNA Origami

So far, we have talked about mechanical features of origami and kirigami, traditionally done with paper. But DNA seems like such a wild possible medium that it shouldn't be possible...right? Well, scientists from Brigham Young University accomplished it by taking single strands of DNA, unzipped from their normal double helix, and were aligned with other strands and then "stapled" together using short pieces of DNA. It ends up being much like a folding pattern we are used to with origami we encounter daily. And, given the right circumstances, you can coax the 2-D material into folding into a 3-D one. Wild! (Bernstein)

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Imagine a material that given the right conditions could origami itself, also as if it were alive. Scientists Marc Miskin and Paul McEuen from Cornell University in Ithaca have done just that with their kirigami design involving graphene. Their material is an atomic scale sheet of silica attached to graphene which maintains a flat shape in the presence of water. But when you add an acid and those silica bits try to absorb it. By carefully picking where to make cuts into graphene and actions happen, as graphene is strong enough to resist the changes in the silica unless compromised in some fashion. This self-deployment concept would be great for a nanobot that needs to be activated in a certain region (Powell).

Who knew that paper folding could be so freaking awesome!

Works Cited

Bernstein, Michael. "DNA 'origami' could help build faster, cheaper computer chips." innovations report, 14 Mar. 2016. Web. 17 Aug. 2020.

Burrows, Leah. “Designing a pop-up future.” Science Daily, 26 Jan. 2016. Web. 15 Jan. 2019.

Horan, James. “The Atomic Theory of Origami.” 31 Oct. 2017. Web. 14 Jan. 2019.

Nishiyama, Yutaka. “Miura Folding: Applying Origami to Space Exploration.” International Journal of Pure and Applied Mathematics. Vol. 79, No. 2.

Powell, Devin. “World’s Thinnest Origami Could Build Microscopic Machines.” Inside Science, 24 Mar. 2017. Web. 14 Jan. 2019.

Wilkins, Alex. "Art of paper cutting inspires light yet strong material." New Scientist. New Scientist, 05 Mar. 2022. Print. 21.

Yiu, Yuen. “The Power of Kirigami.” Inside Science, 28 Apr. 2017. Web. 14 Jan. 2019.

© 2019 Leonard Kelley

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