Cable Kink Analysis: Cable Loop Stability Under Tension

Yabuta, Tetsuro; Yoshizawa, Noriko; Kojima, N.

doi:10.1115/1.3162531

Cited by 16 publications

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“…Neukirch and Henderson made a detailed investigation into the connectivity of solutions for rods subject to end thrusts and coaxial twists [12,13]. Theory, numerics, and experiment show that circular cross section rods, an integrable system, when subject to such boundary conditions will buckle, hockle into a loop, or snarl into a self-contacting twisted structure [14][15][16][17][18][19][20][21][22]. Anisotropic rods, those with preferred bending directions, display even more complicated and potentially non-integrable behavior due to non-conserved twist [23][24][25][26][27][28].…”

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Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations

Hanna

2019

Journal of the Mechanics and Physics of Solids

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Motivated by observations of snap-through phenomena in buckled elastic strips subject to clamping and lateral end translations, we experimentally explore the multi-stability and bifurcations of thin bands of various widths and compare these results with numerical continuation of a perfectly anisotropic Kirchhoff rod. Our choice of boundary conditions is not easily satisfied by the anisotropic structures, forcing a cooperation between bending and twisting deformations. We find that, despite clear physical differences between rods and strips, a naive Kirchhoff model works surprisingly well as an organizing framework for the experimental observations. In the context of this model, we observe that anisotropy creates new states and alters the connectivity between existing states. Our results are a preliminary look at relatively unstudied boundary conditions for rods and strips that may arise in a variety of engineering applications, and may guide the avoidance of jump phenomena in such settings. We also briefly comment on the limitations of current strip models. * jhyutian@vt.edu † hannaj@vt.edu arXiv:1708.05968v2 [cond-mat.soft] 31 Jan 2018 the backbone of the behavior of wider bands. We reveal connections between various states, including higher-order unstable elastica modes and stable twisted states created by the rod's anisotropy.While the Kirchhoff equations show themselves to be a surprisingly useful tool in the analysis of strip behavior, we wish to emphasize that there is no reason to assume that such a model, which assumes that cross sections remain perpendicular to the centerline, would be appropriate for strips. On the other hand, the common assumption that transverse bending of strips is governed by the constraint of developability can lead to difficulties of its own, particularly for narrow strips, issues that we will briefly touch upon in an appendix. Until such issues are resolved, it is advantageous to employ an easily implemented rod model from which the strips inherit most, or even all, of their bifurcations. However, use of such a model should not be taken to imply that a narrow strip is equivalent to a rod.Boundary conditions like those we explore here are potentially of interest in helping to avoid violent snap-throughs of connectors, hinges, and umbilicals in flexible and deployable systems. Geometries similar to ours appear as slipping folds [3] in deployable space membranes, buckled elements in flexible electronics and robotics, and decorative streamers in childrens' toys [4]. Multi-stable structures find use in compliant mechanisms [5] at all length scales. The behavior of strips under our loading conditions is likely related to the phenomenon of lateral-torsional buckling, known to structural engineers [6].There is much prior work on the configurations of naturally straight rods. Work on the general behavior and classification of solutions includes that of Antman [7,8], Maddocks [9], Nizette and Goriely [10], and Cognet and co-workers [11]. Neukirch and Henderson made a detailed investigation...

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confidence: 99%

Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations

Hanna

2019

Journal of the Mechanics and Physics of Solids

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“…The loops can rotate by an angle to relax the excess twist, see Ref. [25] forming a precursor of plectonemic structures (Fig. 1). …”

Section: Charged Filament: Untwisted Ringmentioning

confidence: 99%

Torque-induced deformations of charged elastic DNA rods: thin helices, loops, and precursors of DNA supercoiling

Cherstvy

2011

J Biol Phys

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We study the deformations of charged elastic rods under applied end forces and torques. For neutral filaments, we analyze the energetics of initial helical deformations and loop formation. We supplement this elastic approach with electrostatic energies of bent filaments and find critical conditions for buckling depending on the ionic strength of the solution. We also study force-induced loop opening, for parameters relevant for DNA. Finally, some applications of this nano-mechanical DNA model to salt-dependent onset of DNA supercoiling are discussed.

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“…Coyne (1990) only considered a single loop. Yabuta et al (1982) discussed cable loop stability assuming a single tightly coiled helical turn. Both works assume the unstressed rod to be straight and avoid boundary conditions by assuming the cable to be infinitely long.…”

Section: Introductionmentioning

confidence: 99%

Cascade unlooping of a low-pitch helical spring under tension

Starostin

Heijden

2009

Journal of the Mechanics and Physics of Solids

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We study the force vs extension behaviour of a helical spring made of a thin torsionally-stiff anisotropic elastic rod. Our focus is on springs of very low helical pitch. For certain parameters of the problem such a spring is found not to unwind when pulled but rather to form hockles that pop-out one by one and lead to a highly non-monotonic force-extension curve. Between abrupt loop pop-outs this curve is well described by the planar elastica whose relevant solutions are classified. Our results may be relevant for tightly coiled nanosprings in future micro- and nano(electro)mechanical devices.Comment: 20 pages, 15 figure

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Cable Kink Analysis: Cable Loop Stability Under Tension

Cited by 16 publications

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Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations

Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations

Torque-induced deformations of charged elastic DNA rods: thin helices, loops, and precursors of DNA supercoiling

Cascade unlooping of a low-pitch helical spring under tension

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