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These nonreciprocal metamaterials can benefit applications such as soft robotics, prosthetics, and energy harvesting.

Engineers and scientists at the University of Texas at Austin and the AMOLF institute in the Netherlands have invented mechanical metamaterials that easily transfer motion in one direction while blocking it in the other. The material can be thought of as a mechanical one-way shield that blocks energy from coming in but transmits it going out the other side. The researchers developed the nonreciprocal mechanical materials using metamaterials, which are synthetic materials with properties that cannot be found in nature.

Breaking the symmetry of motion can enable greater control of mechanical systems and improve efficiency. These nonreciprocal metamaterials can potentially be used to realize new types of mechanical devices, such as actuators (components of a machine that are responsible for moving or controlling a mechanism), and other devices that could improve energy absorption, conversion, and harvesting; soft robotics; and prosthetics.

The researchers’ breakthrough lies in the ability to overcome reciprocity, a fundamental principle governing many physical systems. Reciprocity ensures the same response when an arbitrary structure is pushed from opposite directions. This principle governs how signals of various forms travel in space, and explains why a radio or acoustic signal that is sent can also be received. In mechanics, reciprocity implies that motion through an object is transmitted symmetrically — if pushing on side A moves side B by a certain amount, the same motion at side A when pushing B can be expected.

“The mechanical metamaterials we created provide new elements in the palette that material scientists can use to design mechanical structures,” said Andrea Alu, a professor at University of Texas’ Cockrell School of Engineering. “This can be of extreme interest for applications in which it is desirable to break the natural symmetry with which the displacement of molecules travels in the microstructure of a material.”

An artist's rendering of mechanical metamaterials. (Credit: Cockrell School of Engineering)

During the past couple of years, Alu, along with Cockrell School research scientist Dimitrios Sounas and other members of their research team, have made breakthroughs in nonreciprocal devices for electromagnetics and acoustics, including nonreciprocal devices for sound, radio waves, and light. While visiting the AMOLF institute in the Netherlands, they started a collaboration with AMOLF researcher Corentin Coulais who recently has been developing mechanical metamaterials. Their close interaction led to this breakthrough.

The researchers first created a rubber, centimeter-scale metamaterial with a specifically tailored fishbone skeleton design. They tailored its design to meet the main conditions to break reciprocity, namely asymmetry and a response that is not linearly proportional to the exerted force.

“This structure provided us inspiration for the design of a second metamaterial with unusually strong nonreciprocal properties,” Coulais said. “By substituting the simple geometrical elements of the fishbone metamaterial with a more intricate architecture made of connected squares and diamonds, we found that we can break very strongly the conditions for reciprocity, and we can achieve a very large nonreciprocal response.”

The material's structure is a lattice of squares and diamonds that is completely homogeneous throughout the sample, like an ordinary material. However, each unit of the lattice is slightly tilted in a certain way, and this subtle difference dramatically controls the way the metamaterial responds to external stimuli.

“The metamaterial as a whole reacts asymmetrically, with one very rigid side and one very soft side,” Sounas said. “The relation between the unit asymmetry and the soft side location can be predicted by a very generic mathematical framework called topology. Here, when the architectural units lean left, the right side of the metamaterial will be very soft, and vice-versa.”

When the researchers apply a force on the soft side of the metamaterial, it easily induces rotations of the squares and diamonds within the structure, but only in the near vicinity of the pressure point. The effect on the other side is small. Conversely, when they apply the same force on the rigid side, the motion propagates and is amplified throughout the material, with a large effect at the other side. As a result, pushing from the left or from the right results in very different responses, yielding a large nonreciprocity even for small applied forces. The team is looking to leverage these topological mechanical metamaterials for various applications, such as soft robotics, prosthetics, and energy harvesting.

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