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Research Papers

Mechanics of Graded Wrinkling

[+] Author and Article Information
Shabnam Raayai-Ardakani

Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: shraayai@mit.edu

Jose Luis Yagüe

IQS—Grup d'Enginyeria de Materials,
Universidad Ramon Llull,
Barcelona 08017, Spain
e-mail: jose.yague@iqs.url.edu

Karen K. Gleason

Department of Chemical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: kkg@mit.edu

Mary C. Boyce

School of Engineering and Applied Science,
Columbia University,
New York, NY 10027
e-mail: boyce@columbia.edu

1Corresponding author.

Manuscript received September 11, 2016; final manuscript received September 22, 2016; published online October 13, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(12), 121011 (Oct 13, 2016) (10 pages) Paper No: JAM-16-1441; doi: 10.1115/1.4034829 History: Received September 11, 2016; Revised September 22, 2016

The properties and behavior of a surface as well as its interaction with surrounding media depend on the inherent material constituency and the surface topography. Structured surface topography can be achieved via surface wrinkling. Through the buckling of a thin film of stiff material bonded to a substrate of a softer material, wrinkled patterns can be created by inducing compressive stress states in the thin film. Using this same principle, we show the ability to create wrinkled topologies consisting of a highly structured gradient in amplitude and wavelength, and one which can be actively tuned. The mechanics of graded wrinkling are revealed through analytical modeling and finite element analysis, and further demonstrated with experiments.

Copyright © 2016 by ASME
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Figures

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Fig. 1

Schematic of uniform wrinkling

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Fig. 2

Free body diagram of the film with η = L/bL in uniform and graded wrinkling subject to compressive force Pf: (a) side view of either uniform or graded geometry, (b) top view—uniform geometry, and (c) top view—graded geometry with taper angle θ

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Fig. 6

Critical strain normalized by the critical strain for uniform wrinkling versus K and tan θ where η = 5/3 in graded wrinkling

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Fig. 5

Schematic of sample geometry with K = 0.82 on the left and images of the actual samples on the right where (A) corresponds to K = 0.72 and (B) corresponds to K = 0.91

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Fig. 4

Longitudinal cross section of the film; the centerline of the film is referenced as z = 0, and distances are measured from the centerline. Note that film is in compression and buckling, and hence the neutral axis is not central.

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Fig. 3

Strain distribution along the length of the film in graded wrinkling and distribution of the critical eigenvalue in graded wrinkling versus the taper angle and η: (a) strain distribution normalized with the macroscopic strain (δ/L) in uniform wrinkling and graded wrinkling corresponding to the geometries with K = 1, K = 0.91, and K = 0.81; (b) plot of the critical eigenvalue (Λcr) in graded wrinkling normalized by the critical eigenvalue in uniform wrinkling (Λcr,uniform) versus η tan(θ); (c) plot of the critical eigenvalue (Λcr) in graded wrinkling normalized by the critical eigenvalue in uniform wrinkling (Λcr,uniform) versus tan(θ) or different values of η; and (d) plot of the inverse of critical eigenvalue (Λcr) in graded wrinkling normalized by the critical eigenvalue in uniform wrinkling (Λcr,uniform) versus tan(θ) for different values of η

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Fig. 7

Wrinkle evolution in uniform and graded wrinkling for the case of εmacro = 4%: (a) uniform wrinkling—K = 1 and (b) graded wrinkling—K = 0.82

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Fig. 8

Strain profiles in graded wrinkling of a trapezoidal geometry with K = 0.82 and Ef/Es = 100 at three different compressive macroscopic strains. As the third, sixth, and seventh waves are initiating, they all have λ/t = 20.3. Also, λ/t of the third wave decreases by 0.9% as the compressive strain is increased by 0.8%. (a) εmacro = 2.9%, (b) εmacro = 3.5%, and (c) εmacro = 3.7%.

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Fig. 9

Wrinkle profile in uniform and graded wrinkling for the case of εmacro = 4%: (a) K = 1, (b) K = 0.91, and (c) K = 0.82

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Fig. 12

Amplitudes of the waves in graded wrinkling for a trapezoidal geometry with K = 0.91: (a) trend in the amplitudes in graded wrinkling over different εmacro for a trapezoidal geometry with K = 0.91 and (b) Amax of graded wrinkling at different εmacroAmax is the maximum amplitude at each macroscopic strain for a trapezoidal geometry with K = 0.91

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Fig. 13

Amplitudes of the waves in graded wrinkling for a trapezoidal geometry with K = 0.82: (a) trend in the amplitudes in graded wrinkling over different εmacro for a trapezoidal geometry with K = 0.82 and (b) Amax of graded wrinkling at different εmacroAmax is the maximum amplitude at each macroscopic strain for a trapezoidal geometry with K = 0.82

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Fig. 10

Critical wrinkling wavelength for different graded geometries with η = 5/3

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Fig. 11

Strain distribution in wrinkled films. The profiles are at εmacro = 4% and Ef/Es = 100. (a) Uniform wrinkling—K = 1, (b) graded wrinkling—K = 0.91, and (c) graded wrinkling—K = 0.82.

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Fig. 16

Free body diagram of the film and substrate under compressive loading: (a) free body diagram of the film and the substrate and (b) free body diagram of an infinitesimal element in the substrate

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Fig. 14

Images of the experimental results of graded wrinkling on the sample geometry with K = 0.72 and εmacro = 20%

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Fig. 15

Various configurations of graded wrinkling

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