Researchers from the UvA Institute of Physics and ENS de Lyon have made a groundbreaking discovery in the realm of metamaterials. They have unlocked the ability to create materials that possess specific points or lines where they remain undistorted when subjected to stress. Remarkably, these materials also possess the ability to retain a memory of past deformations, such as poking or squeezing. The implications of this achievement extend to fields like robotics, mechanical computers, and even quantum computing.
This advancement revolutionizes the concept of metamaterials, which are materials whose properties are determined by their structure rather than their chemical composition. To engineer a metamaterial with mechanical memory, the team of physicists, comprising Xiaofei Guo, Marcelo Guzmán, David Carpentier, Denis Bartolo, and Corentin Coulais, recognized the necessity for its design to be “frustrated.” This frustration corresponds to a novel form of order, which they have aptly named non-orientable order.
In essence, this research represents a significant leap forward in our understanding and control of materials, opening up a plethora of possibilities for practical applications in various technological domains.
Physics with a twist
Let’s take a simple example to illustrate the concept of non-orientability using a Möbius strip. You can easily create a Möbius strip by taking a strip of paper, giving it a half twist, and then connecting its ends. Try it out at home with a strip of paper and observe the following phenomenon:
When you trace the surface of the Möbius strip with your finger, you’ll notice something peculiar. As you complete a full loop and reach your starting point, your finger will be on the opposite side of the paper. This characteristic distinguishes the Möbius strip as a non-orientable object.
Unlike a regular cylinder, which has distinct inner and outer surfaces, the Möbius strip lacks such differentiation due to its twist. It embodies a unified surface where labeling the two sides consistently becomes impossible.
The implications of non-orientability become apparent when you apply external pressure to objects or metamaterials. If you place a plain cylinder and a Möbius strip on a flat surface and exert pressure from above, the sides of the cylinder will uniformly bulge inward or outward. In contrast, the non-orientability of the Möbius strip prevents such uniform deformation. Instead, it guarantees the existence of a specific point along the strip that remains unaffected by the applied pressure.
This insight, derived by Guo and her colleagues, emphasizes how non-orientability significantly influences the response of an object or metamaterial when subjected to compression or squeezing.
Frustration is not always a bad thing
The implications of this behavior extend beyond Möbius strips, generating great excitement. Coulais, the leader of the Machine Materials Laboratory at the University of Amsterdam, explains, “We have discovered that the behavior of non-orientable objects, like Möbius strips, can be used to describe any globally frustrated material. These materials naturally strive for order, but their structure prevents the order from spanning the entire system, resulting in its disappearance at a specific point or line in space. Regardless of any attempts to eliminate this vanishing point, it remains an inherent characteristic of the structure.”
To demonstrate this concept, the research team designed and 3D-printed their own mechanical metamaterial structures, which exhibit the same frustrated and non-orientable behavior as Möbius strips. Their designs consist of interconnected rings of squares joined by hinges at their corners. When pressure is applied to these rings, adjacent squares rotate in opposite directions, causing their edges to move closer together. This rotational behavior resembles the anti-ferromagnetic ordering observed in certain magnetic materials.
Interestingly, rings composed of an odd number of squares experience frustration since it becomes impossible for all neighboring squares to rotate in opposite directions simultaneously. Consequently, squeezed odd-numbered rings exhibit non-orientable order, mandating that the rotation angle at a specific point along the ring must be zero.
This robust topological property arises from the material’s overall shape. By connecting multiple metarings together, it becomes possible to mimic the mechanical properties of higher-dimensional topological structures, including the renowned Klein bottle.
The ability to design materials with frustrated and non-orientable behavior opens up new avenues for creating innovative metamaterials and exploring their unique properties for various applications.
The presence of a specific point or line where deformation is entirely absent plays a crucial role in imparting mechanical memory to materials. Instead of uniformly squeezing a metamaterial ring, one can apply pressure at distinct points. Interestingly, the order in which these points are pressed determines the location of the point or line with zero deformation.
This intriguing behavior essentially enables information storage. In fact, it can even be utilized to perform certain types of logic gates, which serve as the foundation of computer algorithms. Consequently, a simple metamaterial ring can function as a mechanical computer.
The implications of this study extend far beyond mechanics. The findings suggest that non-orientability can serve as a robust design principle for metamaterials that efficiently store information across various scales, spanning fields such as colloidal science, photonics, magnetism, and atomic physics. Furthermore, it holds promise for the development of novel quantum computers.
Coulais concludes by highlighting the team’s future plans: “Our next focus is leveraging the resilience of these vanishing deformations in the field of robotics. We envision the application of these deformations in the creation of robotic arms and wheels, offering predictable bending and locomotion mechanisms.”
The research, which appears in the journal Nature, marks a significant advancement in our understanding of metamaterials and their potential applications.
Source: University of Amsterdam