Wrinkling of an elastic sheet under tension

Cerda, Enrique; Ravi‐Chandar, K.; Mahadevan, L.

doi:10.1038/419579b

Cited by 341 publications

(311 citation statements)

References 2 publications

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“…where the nonzero elements of the fourth order tensor C solely depend on the nondimensional material parameters: C 1111 = 1, C 1122 = C 2211 = rν [xy] , C 2222 = r and finally C 1212 = q(rν 2 [xy] − 1). To obtain the energy densities Ψ m and Ψ b for orthotropic films we use the linearized bending tensor (5), the finite strain in-plane tensor from (10) and integrate through the thickness of the film:…”

Section: A Model Of Thin Orthotropic Plates Under Finite In-plane Strmentioning

confidence: 99%

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Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Sipos

Fehér

2016

International Journal of Solids and Structures

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Abstract. A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23, 777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the Föppl-von Kármán equations extended to the finite in-plane strain regime. It has also been revealed that for some aspect ratios of the rectangular domain wrinkles do not occur at all regardless of the applied extension. To verify these predictions we carried out experiments on thin (20 µm thick adhesive covered), previously prestressed elastomer sheets with different aspect ratios under displacement controlled pull tests. On one hand the the adjustment of the material properties during prestressing is highly advantageous as in targeted strain regime the film becomes substantially linearly elastic (which is far not the case without prestress). On the other hand a significant, non-ignorable orthotropy develops during this first extension. To enable quantitative comparisons we abandoned the assumption about material isotropy inherent in the original model and derived the governing equations for an orthotropic medium. In this way we found good agreement between numerical simulations and experimental data.Analysis of the negativity of the second Piola-Kirchhoff stress tensor revealed that the critical stretch for a bifurcation point at which the wrinkles disappear must be finite for any aspect ratio. On the contrary there is no such a bound for the aspect ratio as a bifurcation parameter. Physically this manifests as complicated wrinkled patterns with more than one highly wrinkled zones on the surface in case of elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new, finite strain model, since the Föppl-von Kármán equations based on infinitesimal strains do not exhibit such a behavior.

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Section: A Model Of Thin Orthotropic Plates Under Finite In-plane Strmentioning

confidence: 99%

“…in-plane compression is a classical buckling problem [28,11], the somehow counterintuitive occurrence of wrinkles under dominantly tensile loading has become intensively discussed around 2000 [9,2,1]. The mechanical background of the phenomena is well described by the variants of the tension-field theory [24,4].…”

Section: Introductionmentioning

confidence: 99%

Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Sipos

Fehér

2016

International Journal of Solids and Structures

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“…Wrinkles arise from competition between the elastic bending energy of a stiff skin and the elastic energy of deformation of the soft substrate on which it is supported. [2,3,21] For a skin of thickness h and Young's modulus Y skin supported on a substrate of Young's modulus Y sub , minimization of the overall elastic energy yields an equilibrium wrinkle wavelength of l / h 1/3 h, where h / Y skin /Y sub . [2,3,21] For large compressive stresses, it is known that hierarchical wrinkling can occur because the amplitude of the smaller, first generation wrinkles saturate, forming an effective skin that can undergo a similar wrinkling process with wavelengths l / h eff 1/3 h eff , where h eff and h eff are the parameters corresponding to the new effective skin.…”

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confidence: 99%

“…[1][2][3][4] Recently, there has been a resurgence of interest in emulating and leveraging wrinkles for various applications. Polymeric wrinkles are finding increased utility as complex quasiperiodic structures important in applications, including cell-fate studies.…”

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confidence: 99%

Tunable Nanowrinkles on Shape Memory Polymer Sheets

et al. 2009

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Controllable biaxial and uniaxial nanowrinkles (see figure) are fabricated by a simple two‐step approach — metal deposition and subsequent heating — based on shape memory polymer (prestressed polystyrene) sheets. The wavelengths of the wrinkles can be tuned by controlling the thickness of deposited metal. The ready integration of the nanowrinkles into microchannels and their effectiveness in surface enhanced sensing is demonstrated.

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“…The film relieves stress by forming a series of periodic wrinkles in the direction parallel to the applied stress. 26,27 An accompanying longitudinal strain results due to fixed or clamped membrane boundaries that prevent the film from relaxing laterally. Scaling models have been developed to predict the spacing and amplitude of compressive wrinkles as well as their characteristic width.…”

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confidence: 99%

Scanning tunneling microscope study of striated carbon ridges in few-layer epitaxial graphene formed on 4H-silicon carbide (0001¯)

Harrison

Capano

Reifenberger

2010

Applied Physics Letters

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Atomically resolved scanning tunneling microscope images of carbon ridge defects found in few-layer graphene formed on the C-face (0001¯) of 4H-silicon carbide reveal a striated exterior surface formed from out-of-plane distortions of the hexagonal graphene lattice. While ridge formation is likely explained by compressive in-plane stresses coupled with the small values of the bending modulus for few-layer graphene, the striated structure along the ridges argues for a localized unidirectional stress in the material directed along the ridge length.

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Wrinkling of an elastic sheet under tension

Cited by 341 publications

References 2 publications

Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Disappearance of stretch-induced wrinkles of thin sheets: A study of orthotropic films

Tunable Nanowrinkles on Shape Memory Polymer Sheets

Scanning tunneling microscope study of striated carbon ridges in few-layer epitaxial graphene formed on 4H-silicon carbide (0001¯)

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