Researchers from the UvA Institute of Physics and ENS de Lyon have discovered how to design materials that necessarily contain a point or line where the material does not deform under pressure, and even remember how it was stabbed or compressed in the past. These results can be used in robots and mechanical computers, while similar design principles can be used in quantum computers.
The result is a breakthrough in the field of metamaterials: engineered materials whose responses are determined by their structure rather than their chemical composition. To build a metamaterial with mechanical memory, physicists Xiaofei Guo, Marcelo Guzmán, David Carpentier, Denis Bartolo, and Corentin Coulais have realized that its design needs to be “frustrated,” and that frustration corresponds to a new type of system, which they call non-orderable.
Physics with a twist
A simple example of something that is not routable is Möbius tape, which is made by taking a strip of material, adding a half-roll to it and then gluing the ends together. You can try this at home using a strip of paper. By following the surface of the Möbius strip with your finger, you will find that when you return to the starting point, your finger will be on the opposite side of the paper.
The Möbius strip is not steerable because there is no way to distinguish the two sides of the strip in a consistent manner; Winding makes the entire surface one and the same. This is in contrast to a simple roller (a bar without any twists whose ends are glued together), which has a distinct inner and outer surface.
Guo and her colleagues realized that non-direction strongly affects how a metamaterial or body responds to stress or pressure. If you put a simple cylinder and a Möbius tape on a flat surface and press them on top, you will find that the sides of the cylinder all bulge out (or inward), while the sides of a Möbius tape cannot do the same. Instead, the latter’s non-durability ensures that there is a point along the bar where it does not deform under stress.
Frustration isn’t always a bad thing
Interestingly, this behavior extends far beyond the Moebius lines.
“We discovered that the behavior of non-orientable objects such as Möbius slices allows us to globally describe any frustrated material. These materials naturally want to be ordered, but there is something in their structure that prevents ordering to encompass the entire system and forces the ordered pattern to vanish at some point or line in space.” There is no way to get rid of this vanishing point without cutting the structure, so it has to be there no matter what,” explains Colais, who leads the Machine Materials Laboratory at the University of Amsterdam.
The research team designed and 3D-printed their mechanical metamaterials structures that exhibit the same frustrating and unsteerable behavior as Mobius chips. Its designs are based on rings of squares connected by hinges at the corners. When these rings are compressed, adjacent squares will rotate in opposite directions so that their edges come closer together. The antiferromagnetic ordering of the neighbors makes the system respond similar to the antiferromagnetic ordering that occurs in some ferromagnetic materials.
Rings made up of an odd number of squares are aborted, because there is no way for all adjacent squares to rotate in opposite directions. Thus, the odd numbered rings exhibit a non-steerable arrangement, in which the angle of rotation at one point along the ring must go to zero.
Being a feature of the general shape of matter makes this a powerful topological property. By linking many scales together, it is even possible to simulate the mechanisms of higher dimensional topological structures such as the Klein bottle.
Having a zero applied point or deformation line is key to endowing the material with mechanical memory. Instead of squeezing the supermaterial ring on all sides, you can press the ring at distinct points. In doing so, the order in which you hit different points determines where the line ends or the zero deformation point.
This is a form of information storage. It can even be used to implement certain types of logic gates, which are the foundation of any computer algorithm. Thus a simple metamaterial ring can function as a mechanical computer.
Beyond mechanics, the study’s findings suggest that non-steerability could be a powerful design principle for metamaterials that can efficiently store information across scales, in fields as diverse as colloidal science, photonics, magnetism, and atomic physics. It could be useful for new types of quantum computers.
Colais concludes, “Next, we want to exploit the power of vanishing deformations for robots. We believe that vanishing deformations can be used to create robotic arms and wheels with predictable flexing and movement mechanisms.”
Publication of the research in the journal nature.
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