Coiling of an elastic beam inside a disk: A model for spider-capture silk

Elettro, Hervé; Vollrath, Fritz; Antkowiak, Arnaud; Neukirch, Sébastien

doi:10.1016/j.ijnonlinmec.2015.03.008

Cited by 13 publications

(22 citation statements)

References 16 publications

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“…Pseudo-arc-length continuation then enables us to follow the solutions as parameters are varied. In order to compare present three-dimensional (3D) results with two dimensional (2D) solutions studied in [13], we use the same parameters k 3 = 0.9, = 10, f γ = 20, and v 0 = 0.02/ 2 = 2 × 10 −4 , but reduce ρ to ρ = 0.1 thereby bringing the meniscus points closer to the bounding sphere. We start with a straight configuration subject to a large applied tension t = n( /2)· d 3 ( /2).…”

Section: Bifurcation Diagrammentioning

confidence: 99%

“…Another path, called Pt in [13], exists and is composed of configurations which are always planar. These configurations, resembling a second buckling mode, are probably unstable, but using a rod with a flat, rectangular cross-section we were able to stabilize them, see Figure 10.…”

Section: Bifurcation Diagrammentioning

confidence: 99%

“…the two configurations in Figure 8. In [13] a path L 1 , comprising 2D configurations which were looping once inside the sphere, was shown. This path does not fulfill the topological constraint R = 0 and is therefore not plotted in Figures 3 or 4.…”

Section: Bifurcation Diagrammentioning

confidence: 99%

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Elastocapillary Coiling of an Elastic Rod Inside a Drop

Elettro

Grandgeorge

Neukirch

2016

J Elast

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Capillary forces acting at the surface of a liquid drop can be strong enough to deform small objects and recent studies have provided several examples of elastic instabilities induced by surface tension. We present such an example where a liquid drop sits on a straight fiber, and we show that the liquid attracts the fiber which thereby coils inside the drop. We derive the equilibrium equations for the system, compute bifurcation curves, and show the packed fiber may adopt several possible configurations inside the drop. We use the energy of the system to discriminate between the different configurations and find a intermittent regime between two-dimensional and three-dimensional solutions as more and more fiber is driven inside the drop.

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Section: Bifurcation Diagrammentioning

confidence: 99%

Section: Bifurcation Diagrammentioning

confidence: 99%

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Elastocapillary Coiling of an Elastic Rod Inside a Drop

Elettro

Grandgeorge

Neukirch

2016

J Elast

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“…To further explore the mechanical response of the composite system, we also performed detailed numerical computations of equilibrium of an inextensible and flexible elastic filament (28,29,31). The filament, held at both extremities with imposed distance x, is subjected to attracting meniscus forces F γ at entrance and exit of a confining sphere.…”

Section: Significancementioning

confidence: 99%

In-drop capillary spooling of spider capture thread inspires hybrid fibers with mixed solid–liquid mechanical properties

Elettro

Neukirch

Vollrath

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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An essential element in the web-trap architecture, the capture silk spun by ecribellate orb spiders consists of glue droplets sitting astride a silk filament. Mechanically this thread presents a mixed solid-liquid behavior unknown to date. Under extension, capture silk behaves as a particularly stretchy solid, owing to its molecular nanosprings, but it totally switches behavior in compression to now become liquid-like: It shrinks with no apparent limit while exerting a constant tension. Here, we unravel the physics underpinning the unique behavior of this "liquid wire" and demonstrate that its mechanical response originates in the shape-switching of the silk filament induced by buckling within the droplets. Learning from this natural example of geometry and mechanics, we manufactured programmable liquid wires that present previously unidentified pathways for the design of new hybrid solid-liquid materials.bioinspired material | microsystems | fluid-structure interaction | elastocapillarity | spider silk H ybrids made of different materials often display effective properties far exceeding those of their components (1): zinccoated steel is both strong and corrosion-resistant; metal foams (hybrids of metal and air) are stiff, light, and crushable at the same time, making them perfect candidates to absorb energy in a car crash (2, 3). Nature also provides many exquisite examples of hybrid design such as the seashell nacre, both stiff and tough thanks to its inner "brick-and-mortar" structure composed of rigid, though brittle, inclusions surrounded by a crack-arresting soft organic matrix (4), or the bamboo stem with its hollow core and honeycomb-shaped cells that maximize the ratio of bending rigidity over weight (5). A most interesting natural hybrid material is the spider's capture thread, which consists of a core filament that supports glue droplets. Here we report the arresting mechanical behavior of this capture thread, which changes from solid-like in extension to liquid-like in compression. We trace this behavior back to the core filament's buckling inside the droplets. A synthetic version of this natural system then allows us to copy the remarkable properties of spider's capture thread and to manufacture a novel type of hybrid material.Spiders use different kinds of silk to build their webs, and a typical ecribellate orb web combines dry and smooth radial threads with wet and droplet-covered spiral threads (6-10). The adhesive nature of these droplets enables the spiral capture thread to perform its primary function of catching insect prey (6). Apart from being sticky, these capture threads also prove to be particularly resilient to tensile tests: Extensive studies on their mechanical behavior (6, 11) revealed that, when stretched, the thread elongates to three times its web length without breaking and recoils back with no noticeable hysteresis or sagging when relaxed (12). This stretchiness confers spider silk a strength 10-fold that of natural or synthetic rubber (13, 14). These remarkable extensional prop...

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“…To rationalize these observations, we invoke a minimal model based on elastic beam theory, and find agreement with experimental data. Further energetic considerations provide a consistent prediction for the winding criterion.Wetting of liquids on fibrous materials is central to a wide variety of natural and industrial phenomena such as the coalescence of wet hairs [1,2], the drying of textiles [3], the altered mechanical properties of dewy spider silk [4][5][6], the defense mechanism of a species of beetle [7], and the bundling of carbon nanotubes and nanowires during processing [8][9][10][11]. In some of these examples, the fibers are sufficiently flexible that capillary forces induce large-scale deformations -a phenomenon also observed in other geometries such as a drop contacting a flexible solid strip [12].…”

mentioning

confidence: 99%

Elastocapillary bending of microfibers around liquid droplets

et al. 2017

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We report on the elastocapillary deformation of flexible microfibers in contact with liquid droplets. A fiber is observed to bend more as the size of the contacting droplet is increased. At a critical droplet size, proportional to the bending elastocapillary length, the fiber is seen to spontaneously wind around the droplet. To rationalize these observations, we invoke a minimal model based on elastic beam theory, and find agreement with experimental data. Further energetic considerations provide a consistent prediction for the winding criterion.Wetting of liquids on fibrous materials is central to a wide variety of natural and industrial phenomena such as the coalescence of wet hairs [1,2], the drying of textiles [3], the altered mechanical properties of dewy spider silk [4][5][6], the defense mechanism of a species of beetle [7], and the bundling of carbon nanotubes and nanowires during processing [8][9][10][11]. In some of these examples, the fibers are sufficiently flexible that capillary forces induce large-scale deformations -a phenomenon also observed in other geometries such as a drop contacting a flexible solid strip [12]. The bending elastocapillary length L BC = E r 3 /γ is the natural length scale that emerges when balancing elastic bending and capillarity, where E is the Young's modulus of the fiber, r is the fiber radius, and γ is the liquid-air surface tension [1,14]. A slender structure is significantly deformed by capillary forces if the length scale over which these forces act is larger than L BC [1]. To understand the wetting of fibers, several model experiments have been carried out, focusing on droplets between slender flexible structures, where material stiffness and geometry dictate the final wetting configuration [1,[15][16][17][18].Despite its simplicity, even the problem of a single droplet atop an undeformable cylinder is interesting as there are two possible equilibrium states: an axisymmetric "barrel" configuration and a non-axisymmetric "clamshell" [19][20][21][22][23]. It is then not surprising that the case of a flexible fiber interacting with a liquid is a rich subject of study, showcasing complexity and stunning examples of self-assembly [1,5,6,[24][25][26]. In a series of beautiful experiments, droplets were placed on taut elastomeric fibers, and reached the barrel configuration [5,6]. With reduced tension, capillary forces cause the fiber to buckle inside the droplet if the radius of the latter exceeds roughly L BC . As the fiber is slackened, it coils inside the droplet which acts as a windlass to maintain tension. However, for a smaller droplet-to-fiber radius ratio, or for less-wettable conditions, the clam-shell configuration may be more favourable than the barrel [23]. In such a case, a soft fiber may instead wind around the surface of a droplet without experiencing a buckling transition [1]. As argued by Roman and Bico, the reduction in surface energy upon winding exceeds the bending penalty if the droplet radius is larger than ∼ L BC . This is reminiscent of DNA molecul...

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Coiling of an elastic beam inside a disk: A model for spider-capture silk

Cited by 13 publications

References 16 publications

Elastocapillary Coiling of an Elastic Rod Inside a Drop

Elastocapillary Coiling of an Elastic Rod Inside a Drop

In-drop capillary spooling of spider capture thread inspires hybrid fibers with mixed solid–liquid mechanical properties

Elastocapillary bending of microfibers around liquid droplets

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