Engineers can use origami's interlocking ridges and precise folds to build devices that grow larger as they are pulled apart, by reversing the tendency of most materials to thin out as they are stretched.
This kind of technique is drawn from the ancient art of origami and is being used more and more by researchers. Instinct and trial and error have aided the progress of the work. Researchers from Georgia Tech and Princeton Engineering have come up with a formula that looks at how structures can be configured to thin, remain unaffected, or thickness as they are stretched, pushed, or bent.
Kon-Well Wang is a professor of mechanical engineering at the University of Michigan.
According to Wang, the paper creates new tools and paths for the technical community to harness and pursue that will further elevate the functions of advanced origami and metamaterials. The impact is huge.
The general rule for the way a broad class of origami responds to stress was laid out in a paper published in August. The rule applies to the folding of objects from parallelograms. In their article, the researchers use origami to explore how structures respond to mechanical stress, such as how a rectangular sponge swells when squeezed in the middle of its long sides. The material behaves like a stick of chewing gum that thins as it is pulled at both ends, when stretched. There is a ratio of compression along one axis and stretching along the other.
The majority of materials have positive ratios. If you stretch a rubber band before it breaks, it will become thinner and thinner before you know it. There is only one reason to put the cork back in a wine bottle. You would break the bottle if you weren't able to.
The researchers were able to predict how the structures will behave under this type of stress. They used the equations to create structures that grew wide when their ends were pulled, or structures that snapped into domes when bent.
Paulino is a professor of civil and environmental engineering. The effect of geometry is amazing.
The equations were created to understand the property of symmetry in the structures, according to James McInerney, the study's first author. Symmetry is the same under certain changes. If you spin a square 180 degrees around the axis, it will remain the same.
McInerney said things that are symmetrical are likely to change in certain conditions. The researchers were able to come up with a system of equations that governed how the structure would respond to stress.
McInerney said that the process was more complicated than defining the symmetry rules because some of the folds did not follow the rules. He said that the paper being folded obeyed the rules and those out of the plane broke them. He said that they broke the symmetry but in a different way.
Rocklin is an assistant physics professor at the Georgia Tech School of Physics.
If you pull on a thin sheet or slab, it will move in the center. Pringles are usually formed by taking the same sheet and bending it upward. Some materials form domes rather than saddles when pulled on, and that's because they are more dense. The amount of bending is predicted by the amount of thinness. The bending of these origami is very different from other materials. What is that?
Different folding patterns and shapes are what researchers have been trying to define rules for. According to Rocklin, the research team discovered the class wasn't important. The way the folds interacted was the most important thing. The researchers needed to understand how the interaction affected the movement of the whole structure in order to understand why it seemed to defy movement. The bend that moves the sheet into the saddle shape is introduced when artists fold the sheet so that it moves along its plane.
It's a hidden mode that comes with the ride.
The researchers were able to explain the strange mode of the sheet by examining the hidden connection.
The exact opposite is explained by the symmetry of that.
The researchers want to examine more complex systems in the future.
Paulino said they would like to try to make sense of the theory and validation it. The blockfold pattern is intriguing.
The article "Discrete symmetries control geometric mechanics in parallelogram-based origami" was published online in August.
More information: James McInerney et al, Discrete symmetries control geometric mechanics in parallelogram-based origami, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.2202777119 Journal information: Proceedings of the National Academy of Sciences
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