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Register a new userWrithing and hockling instabilities in twisted elastic fibers
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Added by
Kari Dalnoki-Veress
Publication date
2021
fields
Physics
and research's language is
English
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The buckling and twisting of slender, elastic fibers is a deep and well-studied field. A slender elastic rod that is twisted with respect to a fixed end will spontaneously form a loop, or hockle, to relieve the torsional stress that builds. Further twisting results in the formation of plectonemes -- a helical excursion in the fiber that extends with additional twisting. Here we use an idealized, micron-scale experiment to investigate the energy stored, and subsequently released, by hockles and plectonemes as they are pulled apart, in analogy with force spectroscopy studies of DNA and protein folding. Hysteresis loops in the snapping and unsnapping inform the stored energy in the twisted fiber structures.
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Higher efficiency, lower cost refrigeration is needed for both large and small scale cooling. Refrigerators using entropy changes during cycles of stretching or hydrostatically compression of a solid are possible alternatives to the vapor-compression fridges found in homes. We show that high cooling results from twist changes for twisted, coiled, or supercoiled fibers, including those of natural rubber, NiTi, and polyethylene fishing line. By using opposite chiralities of twist and coiling, supercoiled natural rubber fibers and coiled fishing line fibers result that cool when stretched. A demonstrated twist-based device for cooling flowing water provides a high cooling energy and device efficiency. Theory describes the axial and spring index dependencies of twist-enhanced cooling and its origin in a phase transformation for polyethylene fibers.
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We investigate with experiments the twist induced transverse buckling instabilities of an elastic sheet of length $L$, width $W$, and thickness $t$, that is clamped at two opposite ends while held under a tension $T$. Above a critical tension $T_lambda$ and critical twist angle $eta_{tr}$, we find that the sheet buckles with a mode number $n geq 1$ transverse to the axis of twist. Three distinct buckling regimes characterized as clamp-dominated, bendable, and stiff are identified, by introducing a bendability length $L_B$ and a clamp length $L_{C}(<L_B)$. In the stiff regime ($L>L_B$), we find that mode $n=1$ develops above $eta_{tr} equiv eta_S sim (t/W) T^{-1/2}$, independent of $L$. In the bendable regime $L_{C}<L<L_B$, $n=1$ as well as $n > 1$ occur above $eta_{tr} equiv eta_B sim sqrt{t/L}T^{-1/4}$. Here, we find the wavelength $lambda_B sim sqrt{Lt}T^{-1/4}$, when $n > 1$. These scalings agree with those derived from a covariant form of the Foppl-von Karman equations, however, we find that the $n=1$ mode also occurs over a surprisingly large range of $L$ in the bendable regime. Finally, in the clamp-dominated regime ($L < L_c$), we find that $eta_{tr}$ is higher compared to $eta_B$ due to additional stiffening induced by the clamped boundary conditions.
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