The role of extensibility in the birth of a ruck in a rug

Lee, Alpha A.; Gouellec, Clément Le; Vella, Dominic

doi:10.1016/j.eml.2015.08.003

Cited by 9 publications

(9 citation statements)

References 22 publications

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“…Thus, from here on, we refer to the first blister solution as the one that is physically accessible. We note that this subtle, nonmonotonic behavior of the pressure-displacement relation has already been observed in other closely related systems [34,58,59].…”

Section: A Energy and Pressure-displacement Relationsupporting

confidence: 78%

“…At a critical confinement, a transition to a delaminated state occurred. This state was governed by two regimes: one is a central blister that mimics the shape of a heavy elastica [32][33][34], and second is an adhered regime that consists of a sinusoidal decaying pattern, which mimics the shape of a floating elastica [7]. The analysis presented here differs from the above study [27] in two aspects.…”

Section: Introductionmentioning

confidence: 89%

“…2, we plot the height profile on a rigid substrate, Eqs. (34), against the soft substrate one, Eqs. (22) and (23).…”

Section: Formation Of a Boundary Layer At The Edge Of A Large Blistermentioning

confidence: 99%

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Delamination of a thin sheet from a soft adhesive Winkler substrate

et al. 2018

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A uniaxially compressed thin elastic sheet that is resting on a soft adhesive substrate can form a blister, which is a small delaminated region, if the adhesion energy is sufficiently weak. To analyze the equilibrium behavior of this system, we model the substrate as a Winkler or fluid foundation. We develop a complete set of equations for the profile of the sheet at different applied pressures. We show that at the edge of delamination, the height of the sheet is equal to sqrt[2]ℓ_{c}, where ℓ_{c} is the capillary length. We then derive an approximate solution to these equations and utilize them for two applications. First, we determine the phase diagram of the system by analyzing possible transitions from the flat and wrinkled to delaminated states of the sheet. Second, we show that our solution for a blister on a soft foundation converges to the known solution for a blister on a rigid substrate that assumed a discontinuous bending moment at the blister edges. This continuous convergence into a discontinuous state marks the formation of a boundary layer around the point of delamination. The width of this layer relative to the extent length of the blister, ℓ, scales as w/ℓ∼(ℓ_{c}/ℓ_{ec})^{1/2}, where ℓ_{ec} is the elastocapillary length scale. Notably, our findings can provide guidelines for utilizing compression to remove thin biofilms from surfaces and thereby prevent the fouling of the system.

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Section: A Energy and Pressure-displacement Relationsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 89%

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Delamination of a thin sheet from a soft adhesive Winkler substrate

et al. 2018

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“…Lee and al. [9] studied the onset of a ruck in an heavy carpet. In both latter problems the finite compressibility of the sheet is the key assumption to study the birth of the instability: blistering (or rucking) can occur at finite end-end compression, and with finite compressive load.…”

mentioning

confidence: 99%

The delamination of a growing elastic sheet with adhesion

Napoli

Turzi

2017

Meccanica

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We study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth causes residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at which the instability occurs. We show that the critical threshold scales with a single dimensionless parameter that comprises information from the geometry of the sheet, the mechanical parameters of material and the adhesive features of the substrate

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“…The present 1D model, as far as we know, has no applicability in such cases. It is relevant, however, to deformations with cylindrical [15,16] or conical [17] symmetries.…”

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confidence: 99%

Properties of compressible elastica from relativistic analogy

Oshri

Diamant

2016

Soft Matter

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Kirchhoff's kinetic analogy relates the deformation of an incompressible elastic rod to the classical dynamics of rigid body rotation. We extend the analogy to compressible filaments and find that the extension is similar to the introduction of relativistic effects into the dynamical system. The extended analogy reveals a surprising symmetry in the deformations of compressible elastica. In addition, we use known results for the buckling of compressible elastica to derive the explicit solution for the motion of a relativistic nonlinear pendulum. We discuss cases where the extended Kirchhoff analogy may be useful for the study of other soft matter systems.Analogies to dynamical problems have been used to simplify the physics of various condensed-matter systems, ranging from the deformation of elastic bodies to the order-parameter profile across an interface between coexisting phases. A particularly well known example is Kirchhoff's kinetic analogy [1]. In this theory the threedimensional (3D) deformation of a slender elastic rod is reduced to the bending deformation of an incompressible curve, representing the mid-axis of the rod. This problem, in turn, is analogous to the dynamics of a rigid body rotating about a fixed point, where the distance along the curve and its local curvature are analogous, respectively, to time and angular velocity. When the filament is confined to a two-dimensional (2D) plane (the celebrated Euler elastica [2]), the equation of equilibrium coincides with the equation of motion of a physical pendulum [1,19].In the examples above the elastic system was reduced to an indefinitely thin, incompressible body, whose equilibrium shape follows the trajectory of a classical dynamical system. In the present work we show that relaxing the incompressibility constraint introduces terms akin to relativistic corrections to classical dynamics. Within this analogy, the compression modulus, Y , plays the role of the relativistic particle's rest mass, and the bendability parameter (Y /B) 1/2 ≡ h −1 , where B is the bending modulus, is analogous to the speed of light. The limit of an incompressible rod (h → 0) corresponds to the nonrelativistic limit.Despite the relevance to real systems, including compressible fluid membranes [4], there have not been many studies of compressible elastica (see [5] and references therein). Following these works, we consider the 2D deformation of a compressible filament, represented by a planar curve of relaxed length L. The same model applies to thin elastic sheets, as well as fluid membranes [6], provided that they are deformed along a single direction. The deformation away from the flat, stress-free * ozzoshri@tau.ac.il

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The role of extensibility in the birth of a ruck in a rug

Cited by 9 publications

References 22 publications

Delamination of a thin sheet from a soft adhesive Winkler substrate

Delamination of a thin sheet from a soft adhesive Winkler substrate

The delamination of a growing elastic sheet with adhesion

Properties of compressible elastica from relativistic analogy

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