Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles

Goldstein, Raymond E.; Warren, Patrick B.; Ball, Robin C.

doi:10.1103/physrevlett.108.078101

Cited by 18 publications

(11 citation statements)

References 17 publications

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“…The mechanics of thin rods has a long history [15,16,17], and is used to tackle a number of problems from different fields today, such as the morphogenesis of slender objects [18,19], the equilibrium shape of elongated biological filaments -such as DNA [20] and bacterial flagellum [21] -and the mechanics of the human hair [22,23]. The classical theory of rods, known as Kirchhoff's rod theory, assumes that all dimensions of the cross-section are comparable: the consequence is that the cross-sections of the rod deform almost rigidly as long as long as the strain remains small.…”

Section: Introductionmentioning

confidence: 99%

A non-linear rod model for folded elastic strips

Dias

Audoly

2014

Journal of the Mechanics and Physics of Solids

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We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of elastic plates, we derive a Kirchhoff rod model for the folded strip. A non-linear effective constitutive law incorporating the underlying geometrical constraints is derived, in which the angle the ridge appears as an internal degree of freedom. By contrast with traditional thin- walled beam models, this constitutive law captures large, non-rigid deformations of the cross-sections, including finite variations of the dihedral angle at the ridge. Using this effective rod theory, we identify a buckling instability that produces the out-of-plane configurations of the folded strip, and show that the strip behaves as an elastic ring having one frozen mode of curvature. In addition, we point out two novel buckling patterns: one where the centerline remains planar and the ridge angle is modulated; another one where the bending deformation is localized. These patterns are observed experimentally, explained based on stability analyses, and reproduced in simulations of the post-buckled configurations

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Section: Introductionmentioning

confidence: 99%

A non-linear rod model for folded elastic strips

Dias

Audoly

2014

Journal of the Mechanics and Physics of Solids

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“…The first two terms are like those of an elastic filament under an aligned gravitational load, with an internal tension varying linearly from one end to the other [46,47].…”

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confidence: 99%

Swirling Instability of the Microtubule Cytoskeleton

Stein

Canio

Lauga

et al. 2020

Preprint

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In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly D. melanogaster have shown a transition from a spatially-disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a swirling instability to spontaneous large-scale rotational motion, as observed.

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“…-Introduction: Contact between slender objects gives rise to complex structures and behaviors in nature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], including DNA ejection from bacteriophages [2], the folding of sheet-like tissues in developmental biology [3,4], and the coiling of plant tendrils or roots [5][6][7]. Examples in daily life [16][17][18][19][20][21][22][23][24][25] include hair brushing, arranging pony tails [16], applying gift-wrap ribbons [17], tying shoelaces [18], rucks in a rug [19,20], coiling elastic or liquid ropes [21][22][23][24][25], or the use of polymer brushes [26], biomimetics [27][28][29][30][31] and coiled tubing in industry…”

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confidence: 99%

Slip Morphology of Elastic Strips on Frictional Rigid Substrates

2017

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The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which-when the bending elasticity dominates over the effect of gravity-are classified into three distinct types of states: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strain and the coefficient of static friction. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb-Amontons friction law and find excellent quantitative agreement with simulations and controlled physical experiments. We also discuss the effect of gravity in order to bridge the difference in the qualitative behaviors of stiff strips and flexible strings or ropes. Our study thus complements recent work on elastic rope coiling and takes a significant step towards establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface.

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Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles

Cited by 18 publications

References 17 publications

A non-linear rod model for folded elastic strips

A non-linear rod model for folded elastic strips

Swirling Instability of the Microtubule Cytoskeleton

Slip Morphology of Elastic Strips on Frictional Rigid Substrates

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