“This has been exploited by a number of experimental groups recently to create prototypical artificial muscle fibers. But how the topology, geometry and mechanics of these slender fibers come together during this process was not completely clear. Our study explains the theoretical principles underlying these shape transformations, and sheds light on the underlying design principles,” said L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology and Physics at Harvard University.
Soft fibers, or filaments, are capable of stretching, shearing, bending or twisting. Researchers from the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) studied how these movements interact in forming knots, braids and helices. According to the team, understanding these can help us to better understand the design of soft actuators.
“Soft fibers are the basic unit of a muscle and could be used in everything from robotics to smart textiles that can respond to stimuli such as heat or humidity,” said Nicholas Charles, a PhD student in Applied Mathematics and first author of the paper. “The possibilities are endless, if we can understand the system. Our work explains the complex morphology of soft, strongly stretched and twisted fibers, and provides guidelines for the best designs.”
To study the physical properties of soft fibers, the team took filament and applied a downward axial load to the filament’s bottom end. It was then twisted while the axial load on the filament’s bottom end was kept constant. After an amount of twist was applied, the filament buckled into what the researchers called a “loopy plectoneme.” The team explained the principle this way: “Imagine stretching and twisting a rubber band as tight as you can. As the twist gets tighter and tighter, part of the band will pop out of the plane and start twisting around itself into a coil or knot. These coils and loops, in the right form, can be harnessed to actuate the knotted fiber.”
“This research gives us a simple way to predict how soft filaments will respond to twisting and stretching,” added Charles.
The team also expressed the significance of their study in future applications. “Going forward, our work might also be relevant in other situations involving tangled filaments, as in hair curls, polymer dynamics and the dynamics of magnetic field lines in the sun and other stars,” said Mahadevan.
The research can be found in Physical Review Letters.