Designers of Materials imbue Frustration to Create Mechanical Memory.

Researchers from the UvA Institute of Physics and ENS de Lyon have unveiled an innovative way to design materials that have a stress point or line where the material doesn’t deform, thereby memorizing how they have been compressed or poked. These materials could have multiple applications in the field of robotics, mechanical computers and even in quantum computing.

The study marks a breakthrough in the field of metamaterials: designer materials whose responses are determined by their structure rather than their chemical composition, offering new opportunities for innovation. To build a metamaterial with mechanical memory, physicists Xiaofei Guo, Marcelo Guzmán, David Carpentier, Denis Bartolo, and Corentin Coulais realized that its design needs to be “frustrated.” This frustration corresponds to a new type of order, which they call non-orientable order.

Revolutionary Design Principles

A Möbius strip is a simple example of a non-orientable object. A Möbius strip is created by taking a strip of material, adding half a twist to it, and then gluing its ends together. Such objects can’t be consistently labeled on both sides, making it one of a kind. The entire surface of the strip remains indistinguishably the same, and it can’t be separated into inner and outer surfaces, unlike a simple cylinder.

The non-orientability strongly affects how the material responds to pressure. If you place a simple cylinder and a Möbius strip on a flat surface and press down on them from above, the sides of the cylinder will bulge out or inwards, while the sides of the Möbius strip won’t deform. The non-orientability of the Möbius strip ensures that there is always a point along the strip that doesn’t deform under pressure.

Frustration is an Opportunity for Innovation

The research team discovered that non-orientable objects exhibit unique behavior, allowing them to describe any material that is globally frustrated. These materials want to be ordered naturally, but their structure prevents them from being symmetric. The ordered pattern vanishes at a point or line in space where the vanishing point can’t be eliminated without cutting the construction.

The designers of the research team created and 3D-printed their own non-orientable mechanical metamaterial structures by designing rings of squares connected by hinges in their corners. When the rings are squeezed, neighboring squares rotate in opposite directions, moving their edges closer together. The system’s response is analogous to the ordering of anti-ferromagnetic materials. Odd-numbered rings are frustrated because there’s no way for all the adjacent squares to rotate in opposite directions. They exhibit non-orientable behavior in which the rotation angle at one point along the ring must go to zero and must exist there, which is a characteristic of the material as a whole.

The design property makes this a strong topological attribute. By binding various metarings together, the mechanics of higher-dimensional topological structures like the Klein bottle can be imitated.

Mechanical Memory

Mechanical memory is the key to providing materials with an enforced point or line of zero deformation. Instead of squeezing the metamaterial ring from all sides, different points on the ring can be pressed. Where the zero deformation point or line ends up is determined by the order in which you touch different points, and this is a means of storing information. It’s also a way to perform some types of logic gates, which are the basis of any computer algorithm. Thus, a simple metamaterial ring can function as a mechanical computer system.

Non-orientability could be a sturdy design principle for metamaterials capable of storing information across scales in different fields like colloidal science, photonics, magnetism, and atomic physics, far beyond mechanics and it would even be valuable for new types of quantum computers.

Coulais, who leads the Machine Materials Laboratory at the University of Amsterdam, concludes, “Next, we want to exploit the robustness of the vanishing deformations for robotics. We believe the vanishing deformations could be used to create robotic arms and wheels with predictable bending and locomotion mechanisms.”

The study was published in the journal Nature.

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