On the buckling of elastic rings by external confinement

Hazel, Andrew L.; Mullin, T.

doi:10.1098/rsta.2016.0227

Cited by 19 publications

(14 citation statements)

References 29 publications

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“…Each W m branch ultimately results in self-contact and at this point the continuation is terminated. Self-contact forces can be included as in [30,33], see also [14,34], but this has not been done here.…”

Section: Numerical Continuation: 5 = 576mentioning

confidence: 99%

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Pressure-driven wrinkling of soft inner-lined tubes

Foster¹,

Verschueren²,

Knobloch³

et al. 2022

New J. Phys.

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A simple equation modelling an inextensible elastic lining of an inner-lined tube subject to an imposed pressure difference is derived from a consideration of the idealised elastic properties of the lining and the pressure and soft-substrate forces. Two cases are considered in detail, one with prominent wrinkling and a second one in which wrinkling is absent and only buckling remains. Bifurcation diagrams are computed via numerical continuation for both cases. Wrinkling, buckling, folding, and mixed-mode solutions are found and organised according to system-response measures including tension, in-plane compression, maximum curvature and energy. Approximate wrinkle solutions are constructed using weakly nonlinear theory, in excellent agreement with numerics. Our approach explains how the wavelength of the wrinkles is selected as a function of the parameters in compressed wrinkling systems and shows how localised folds and mixed-mode states form in secondary bifurcations from wrinkled states. Our model aims to capture the wrinkling response of arterial endothelium to blood pressure changes but applies much more broadly.

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Section: Numerical Continuation: 5 = 576mentioning

confidence: 99%

“…In contrast, compressed or deflated spherical shells [8,9] exhibit buckling with no preferred length scale, as do elastic rings supporting a soap film [10][11][12][13]. Constrained buckling of elastic rings exhibits similar properties [14].…”

Section: Introductionmentioning

confidence: 99%

Pressure-driven wrinkling of soft inner-lined tubes

Foster¹,

Verschueren²,

Knobloch³

et al. 2022

New J. Phys.

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show abstract

“…This problem is also the simplest problem for the study of interacting elastic bodies in large deformations. While the interaction of a single elastic rings inside a hard ring has been studied extensively [3][4][5][6] as a paradigm for elastic materials under confinement [7], the problem of two interacting elastic rods has received little attention (see, however, the interesting early work on the self-interaction of a rod in the plane [8] and recent work on self-encapsulation [9]).…”

Section: Introductionmentioning

confidence: 99%

A tale of two nested elastic rings

Napoli

Goriely

2017

Proc. R. Soc. A.

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Elastic rods in contact provide a rich paradigm for understanding shape and deformation in interacting elastic bodies. Here, we consider the problem of determining the static solutions of two nested elastic rings in the plane. If the inner ring is longer than the outer ring, it will buckle creating a space between the two rings. This deformation can be further influenced by either adhesion between the rings or if pressure is applied externally or internally. We obtain an exact solution of this problem when both rings are assumed inextensible and unshearable. Through a variational formulation of the problem, we identify the boundary conditions at the contact point and use the Kirchhoff analogy to give exact solutions of the problems in terms of elliptic functions. The role of both adhesion and pressure is explored.

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“…While other higher modes of instability exist, they have only been observed by the imposition of an additional breaking of symmetry, e.g. via confinement with a polygonal boundary of the desired mode number [19]. For thin, unconfined elastic annuli, static wrinkling patterns with higher modes of instability are common [4,5,20,21], but require two opposing (though not in general equal) tensions to be applied: when T out /T in 1 in these static systems, the annulus breaks its gross axisymmetry by forming a lenticular or 'stadium' shape [21].…”

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confidence: 99%

Dynamic buckling of elastic rings in a soap film

Box,

Kodio,

O'Kiely

et al. 2018

Preprint

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Dynamic buckling may occur when a load is rapidly applied to, or removed from, an elastic object at rest. In contrast to its static counterpart, dynamic buckling offers a wide-range of accessible patterns depending on the parameters of the system and the dynamics of the load. To study these effects, we consider experimentally the dynamics of an elastic ring in a soap film when part of the film is suddenly removed. The resulting change in tension applied to the ring creates a range of interesting patterns that cannot be easily accessed in static experiments. Depending on the aspect ratio of the ring's cross section, high-mode buckling patterns are found in the plane of the remaining soap film or out of the plane. Paradoxically, while inertia is required to observe these non-trivial modes, the selected pattern does not depend on inertia itself. The evolution of this pattern beyond the initial instability is studied experimentally and explained through theoretical arguments linking dynamics to pattern selection and mode growth. We also explore the influence of dynamic loading and show numerically that by imposing a rate of loading that competes with the growth rate of instability, the observed pattern can be selected and controlled.

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On the buckling of elastic rings by external confinement

Cited by 19 publications

References 29 publications

Pressure-driven wrinkling of soft inner-lined tubes

Pressure-driven wrinkling of soft inner-lined tubes

A tale of two nested elastic rings

Dynamic buckling of elastic rings in a soap film

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