By finding those symmetries in the origami, the researchers were able to create a system of equations that governed how the structure would respond to stress. “Things that are symmetrical deform in expected ways in certain conditions,” McInerney said. For example, if you spin a square 180 degrees around an axis running between the centers of two sides, its shape remains the same. Symmetry means something that remains the same under certain transformation. James McInerney, who is the study’s first author and a postdoctoral researcher at the University of Michigan, said the team created the equations to understand the property of symmetry in the structures. “With origami you can do this,” said Paulino, who is a professor of civil and environmental engineering and the Princeton materials institute. They then used the equations to create origami structures with a negative Poisson ratio – origami structures that grew wide instead of narrower when their ends were pulled, or structures that snapped into dome shapes when bent instead of sagging into a saddle shape. The researchers were able to write a set of equations to predict how origami-inspired structures will behave under this kind of stress. “Cork has a zero Poisson ratio, and that is the only reason you can put the cork back in a wine bottle. If, for example, you pick up a rubber band and stretch it, it will become thinner and thinner before it breaks,” said Glaucio Paulino, professor at Princeton. “Most materials have a positive Poisson ratio. The ratio of compression along one axis with stretching along the other is called the Poisson ratio. Of particular interest was how materials behave when stretched, like a stick of chewing gum that thins as it is pulled at both ends. In their article, the researchers use origami to explore how structures respond to certain kinds of mechanical stress – for example, how a rectangular sponge swells in a bowtie shape when squeezed in the middle of its long sides. The rule applies to origami formed from parallelograms (such as a square, rhombus, or rectangle) made of thin material. In a paper published August 3 in the Proceedings of the National Academy of Sciences, the researchers lay out their general rule for the way a broad class of origami responds to stress. Now, researchers from Princeton Engineering and Georgia Tech have developed a general formula that analyzes how structures can be configured to thin, remain unaffected, or thicken as they are stretched, pushed, or bent. However, much of the work has progressed via instinct and trial and error. Researchers increasingly use this kind of technique, drawn from the ancient art of origami, to design spacecraft components, medical robots, and antenna arrays. Most materials – from rubber bands to steel beams – thin out as they are stretched, but engineers can use origami’s interlocking ridges and precise folds to reverse this tendency and build devices that grow wider as they are pulled apart.
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