Wrinkle formations in axi-symmetrically stretched membranes

Géminard, Jean‐Christophe; Bernal, Roberto; Melo, Francisco

doi:10.1140/epje/i2004-10041-1

Cited by 75 publications

(92 citation statements)

References 12 publications

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“…In order to study carefully the properties of the emerging structures, we focus on bilayer systems compressed uniaxially in the plane of the rigid membrane that have been intensively studied. [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63] Notice, however, that more complex geometries have already been studied by considering biaxial/radial stresses (with or without substrate) or curved substrates [64][65][66][67][68][69][70][71] where wrinkle to fold transitions can also be observed for large enough deformations of the systems.…”

Section: -47mentioning

confidence: 99%

Wrinkle to fold transition: influence of the substrate response

et al. 2013

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Spatially confined rigid membranes reorganize their morphology in response to imposed constraints. Slight compression of a rigid membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad spatial distribution of energy. For larger compression, the deformation energy is progressively localized in small regions which ultimately develop sharp folds. We review the influence of the substrate on this wrinkle to fold transition by considering two models based on purely viscous and purely elastic foundations. We analyze and contrast the physics and mathematics of both systems.

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Section: -47mentioning

confidence: 99%

Wrinkle to fold transition: influence of the substrate response

et al. 2013

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“…They have important applications in micro-engineering such as the formation of controlled patterns [5], or the estimation of mechanical properties from the number and the extent of the wrinkles [6][7][8][9]. While most studies have focused on near threshold patterns, recent contributions have pushed further the description of finely wrinkled plates, i.e., well above the initial buckling threshold [10,11].…”

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Stamping and Wrinkling of Elastic Plates

Hure¹,

Roman²,

Bico³

2012

Phys. Rev. Lett.

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We study the peculiar wrinkling pattern of an elastic plate stamped into a spherical mold. We show that the wavelength of the wrinkles decreases with their amplitude, but reaches a maximum when the amplitude is of the order of the thickness of the plate. The force required for compressing the wrinkled plate presents a maximum independent of the thickness. A model is derived and verified experimentally for a simple one-dimensional case. This model is extended to the initial situation through an effective Young modulus representing the mechanical behavior of wrinkled state. The theoretical predictions are shown to be in good agreement with the experiments. This approach provides a complement to the "tension field theory" developed for wrinkles with unconstrained amplitude.Wrinkling patterns are observed when thin plates are put under compression, spanning scales from geological patterns [1], skin wrinkles resulting from aging processes or scars [2,3] to cells locomotion generating strains on substrates [4]. They have important applications in micro-engineering such as the formation of controlled patterns [5], or the estimation of mechanical properties from the number and the extent of the wrinkles [6][7][8][9]. While most studies have focused on near threshold patterns, recent contributions have pushed further the description of finely wrinkled plates, i.e., well above the initial buckling threshold [10,11]. These studies consider plates submitted to strong in-plane tension on the boundaries, which prevents stress focusing commonly observed in crumpled paper [12]. In these descriptions, wrinkles are assumed to totally relax compressive stresses, as in traditional tension field theory [13,14]. In addition, both amplitude and wavelength of the wrinkles vanish with the thickness of the plate. We propose to study a conceptually different wrinkling regime where the boundaries are free from tension but the amplitude of the wrinkles is highly constrained. We focus on the simplest example, an elastic plate compressed in a spherical mold with a confinement defined by a gap δ (Fig. 1). This stamping configuration is common in industrial processes where metal plates are plastically embossed, the mismatch in Gaussian curvature generally leading to regular wrinkles [15][16][17]. In the elastic case, crumpling singularities first appear as the mold is progressively closed down (Fig. 1c) and evolve into a pattern of apparently smooth radial wrinkles for high confinement (Fig. 1d-e). We show that constraining the amplitude does not lead to the collapse of compressive stress. Instead, the wrinkling pattern derives from a nontrivial balance between compression and bending stresses, with surprising consequences : the wavelength of the wrinkles does not vanish and the constraining force reaches a maximum independent of the thickness of the plate.One-dimensional problem. We start by considering the simpler problem of a plate of length L, thickness h and unit width. In-plane displacements are imposed at both ends u x (±L/2) = ±∆/2 (Fig...

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“…3 The systems that most commonly exhibit the wrinkling phenomenon are textiles, skin, and thinner coatings by mismatch. 4 In applications to large structures, the pre-stressed thin membranes are a key element in the next generation of spacecraft, such as solar sails, sunshields, solar collectors, and gossamer structures. 5,6 Wrinkling instability has recently been used as a versatile patterning platform to create unique surface patterns for a wide range of applications related to surface topography and its dynamic tuning.…”

Section: Introductionmentioning

confidence: 99%

Wrinkling of extensional thin films through modified large deflection equations analytically and experimentally

Jen

2015

AIP Advances

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The stretch-induced wrinkling of thin films is solved through the modified von Kármán large deflection equations by first selecting the suitable deformation expressions that satisfy boundary conditions. Then, adopting the principle of minimum potential energy we obtain the deformations of simply supported rectangular thin films. The obtained significant deflections are nonlinearly elastic and of the lowest order of infinite solutions. The parameters of aspect ratio, the thickness and material of thin films are studied analytically and numerically. The highlighted results of wrinkle amplitude and load are in good agreement with experiments. The methodology also indicates the limit load impending plasticity and predicts the applied load precisely for each wrinkle. Further, it can be extended to the variety of multifunctional orthotropic and multi-layered thin films.

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Wrinkle formations in axi-symmetrically stretched membranes

Cited by 75 publications

References 12 publications

Wrinkle to fold transition: influence of the substrate response

Wrinkle to fold transition: influence of the substrate response

Stamping and Wrinkling of Elastic Plates

Wrinkling of extensional thin films through modified large deflection equations analytically and experimentally

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