Giving a twist to the design of metamaterials and squeezing out novel applications

Have you tried to twist a rubber tube, like a watering hose? If the tube is soft, it buckles and distorts the flow through the hose (Video 1-left). This mechanical instability is known as torsional buckling, which can occur in various systems of different length scales, from aircraft wings to blood veins. Preventing this buckling has been challenging for soft systems so far. 
We spotlight a design strategy to prevent this torsional buckling. Our architected cylindrical shells (meta-shells) promote uniform squeezing upon twisting (Video 1-right). This unique behavior prevents its buckling even under surprisingly large twist angles, more than 360°. The design strategy relies on two essential characteristics of the material.  

Video 1. Torsional buckling versus squeezing: Twisting yields buckling
in a rubber tube (left) and squeezing in a meta-shell (right).
 

Design principles
The first characteristic is the negative Poisson’s ratio. It is a known fact that compressing a piece of rubber in one direction makes it expand in other directions, like when you squeeze mochi squishy. This behavior is due to the positive Poisson’s ratio of typical materials. However, architected materials can behave oppositely; compressing these materials in one direction causes contraction in the lateral direction (Video 2). Such architected systems are known as metamaterials and typically are composed of a periodic network of rationally designed building blocks (unit cells). If metamaterials display a negative Poisson’s ratio, they are called auxetic metamaterials. A famous type of auxetic metamaterials is made by simply implementing a 2D array of closely packed circular holes on a sheet, giving them the memorable name of the holey sheet (Video 2). This pattern can be employed in cylindrical geometry to create cylindrical metamaterials (meta-shells). 

Video 2. Auxetic holey sheet. 

The second characteristic is the tiling of the unit cells with a helical periodicity on our meta-shells (helical meta-shells). We achieve helical periodicity by rotating the unit cell network from its vertical position (Figure 1). This helical periodicity gives rise to meta-shells behaving significantly differently than the nonhelical meta-shells.  

Figure 1. Nonhelical (left) versus helical (right) meta-shell.

We discovered that the combination of helical periodicity and auxeticity enables these helical meta-shells to prevent torsional buckling. In fact, auxeticity is triggered upon twist due to helical periodicity. In this scenario, the twist induces a uniform radial squeezing (negative radial strain). Unit cells rearrange during the torsion, fill the voids, and become tightly packed. These meta-shells’ stability is enhanced by uniform radial squeezing and densification. These transitions lead to the circumvention of the torsional buckling.

Applications 

The mechanism of the radial squeezing under twist can be employed to design twist-driven compressors. We introduce a twist-driven compressor to generate pulsatile flow, which works through a cyclic twist-and-release mechanism applied to our meta-shell (Video 3-left). This cyclic driving leads to a pump system that may offer advantages compared to other pumping systems. In general, twist motors are more common and simple to function. Additionally, it might be easier to use the twist-driven compressor in scenarios with limited space or cylindrical constraints.  
Furthermore, we demonstrate that meta-shells with multiple helicities allow for designing squeezing at desired locations upon twist. For example, in a meta-shell with opposite chirality at the top and bottom half, a clockwise twist squeezes the bottom part whereas the counterclockwise twist squeezes the top part (Video 3-right).  

Video 3. Twist-driven pulsatile pumping (left). Local squeezing in a meta-shell with opposite helicities at the lower and upper half (right).

In addition to twist-driven compressors, this mechanism may inspire other applications in designing soft robots, machine materials, and even biological systems functioning under twist deformation. 
Conclusion
In conclusion, we demonstrate a methodology to program stability in materials. We feature cylindrical meta-shells that display radial squeezing when twisted and effectively circumvent torsional buckling. Finally, we demonstrate how twist-driven squeezing is applicable for designing functional and novel compressing systems.