Non-symmetric localized fold of a floating sheet

Rivetti, Marco

doi:10.1016/j.crme.2013.01.005

Cited by 21 publications

(31 citation statements)

References 24 publications

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“…On the other hand, Rivetti and Antkowiak [23,28] have observed the exact solutions of the model presented here [22][23][24]. The large size system-the characteristic length is l ∼ 1 cm-used in their experiment appears to be accurately described by bending and gravity only, and is thus likely to exhibit the folding behavior predicted here.…”

Section: Discussionmentioning

confidence: 72%

Mechanics of large folds in thin interfacial films

2014

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A thin film confined to a liquid interface responds to uniaxial compression by wrinkling, and then by folding, that has been solved exactly before self-contact. Here, we address the mechanics of large folds, i.e., folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers or capillary rafts, we discuss how to incorporate film weight, self-adhesion, or energy dissipation.

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Section: Discussionmentioning

confidence: 72%

Mechanics of large folds in thin interfacial films

2014

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“…Exactly solvable problems often * hdiamant@tau.ac.il † t-witten@uchicago.edu owe their integrability to extra symmetries. In the current work, we focus on the corresponding extra symmetry in the fluid-supported sheet, which is manifest in a continuous degeneracy of ground states [24,25]. We connect this peculiar property of the one-dimensional buckling problem to the simple translational symmetries of the two-dimensional sine-Gordon problem.…”

Section: Introductionmentioning

confidence: 99%

Shape and symmetry of a fluid-supported elastic sheet

Diamant

Witten²

2013

Phys. Rev. E

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A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross section of the position-time sine-Gordon amplitude profile. Here we show that when one system is embedded in a higher-dimensional system in this way, obvious symmetries in the larger system can lead to nontrivial symmetries in the embedded system. In particular, a thin buckled membrane on a fluid substrate has a continuous degeneracy that interpolates between a symmetric and an antisymmetric fold. We find the Hamiltonian generator of this symmetry and the corresponding conserved momentum by interpreting the simple translational symmetries of the sine-Gordon chain in terms of the embedded coordinates. We discuss possible extensions to other embedded dynamical systems.

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“…We also compute the free energy of these structures, and identify structures corresponding to minima of the free energy with the stable states observed in experiments. Our results can be considered to be an extension of the work of [2,21] to finite domains and extend the analysis in [5,22] to multifold states.…”

Section: Introductionmentioning

confidence: 64%

“…When l is not divisible by m the folds forming the array become distorted and resemble the family of arbitrary phase folds described in [21] for an infinite length sheet. The rule (b) for the local shape of each fold can be understood in terms of the phase ϕ f in Eq.…”

Section: Multifold Solutionsmentioning

confidence: 97%

“…Thus the symmetric and antisymmetric solutions correspond to the particular cases ϕ f = π/2 and ϕ f = 0, respectively. The asymmetric family (ϕ f = 0, π/2) has been shown to describe the shape of an elastic sheet when extracted from a fluid bath [21]. On the other hand, periodic solutions on an infinite sheet can be found in terms of Jacobi elliptic functions,…”

Section: B Exact Solutions For An Infinite Sheetmentioning

confidence: 99%

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Fluid-supported elastic sheet under compression: Multifold solutions

Gordillo

Knobloch

2019

Phys. Rev. E

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The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and antisymmetric states are computed and the corresponding bifurcation diagrams determined. Weakly nonlinear analysis is used to analyze the transition from periodic wrinkles to single fold and multifold states and to compute their energy. States with the same number of folds have energies that barely differ from each other and the energy gap decreases exponentially as localization increases. The stability properties of the different competing states are established and provide a basis for the study of fold interactions.

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Non-symmetric localized fold of a floating sheet

Cited by 21 publications

References 24 publications

Mechanics of large folds in thin interfacial films

Mechanics of large folds in thin interfacial films

Shape and symmetry of a fluid-supported elastic sheet

Fluid-supported elastic sheet under compression: Multifold solutions

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