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Research Papers

Mechanism of Surface Wrinkle Modulation for a Stiff Film on Compliant Substrate

[+] Author and Article Information
Yilun Liu

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace Engineering,
Xi’an Jiaotong University,
No. 28, Xianning West Road,
Xi’an, Shaanxi 710049, China;
Shaanxi Engineering Research Center
of Nondestructive Testing
and Structural Integrity Evaluation,
Xi’an Jiaotong University,
No. 28, Xianning West Road,
Xi’an, Shaanxi 710049, China
e-mail: yilunliu@mail.xjtu.edu.cn

Mengjie Li

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace Engineering,
Xi’an Jiaotong University,
No. 28, Xianning West Road,
Xi’an, Shaanxi 710049, China;
Shaanxi Engineering Research Center of
Nondestructive Testing and Structural
Integrity Evaluation,
Xi’an Jiaotong University,
No. 28, Xianning West Road,
Xi’an, Shaanxi 710049, China
e-mail: limengjieab@stu.xjtu.edu.cn

Jingran Liu

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace Engineering,
Xi’an Jiaotong University,
No. 28, Xianning West Road,
Xi’an, Shaanxi 710049, China;
Shaanxi Engineering Research Center of Nondestructive Testing
and Structural Integrity Evaluation,
Xi’an Jiaotong University,
No. 28, Xianning West Road,
Xi’an, Shaanxi 710049, China
e-mail: liujingran@stu.xjtu.edu.cn

Xi Chen

ASME Fellow
Columbia Nanomechanics Research Center,
Department of Earth and Environmental
Engineering,
Columbia University,
500 West 120th Street,
New York, NY 10027
e-mail: xichen@columbia.edu

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 25, 2017; final manuscript received March 12, 2017; published online April 5, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(5), 051011 (Apr 05, 2017) (9 pages) Paper No: JAM-17-1110; doi: 10.1115/1.4036256 History: Received February 25, 2017; Revised March 12, 2017

In this work, the surface wrinkle modulation of the film/substrate system caused by eigenstrain in the film is studied. A theoretical model is proposed which shows the change of the wrinkle amplitude is completely determined by four dimensionless parameters, i.e., the eigenstrain in the film, the plane strain modulus ratio between the film and the substrate, the film thickness to wrinkle wavelength ratio, and the initial wrinkle amplitude to wavelength ratio. The surface wrinkle amplitude becomes smaller (even almost flat) for the contraction eigenstrain in the film, while for the expansion eigenstrain it becomes larger. If the expansion eigenstrain exceeds a critical value, secondary wrinkling on top of the existing one is observed for some cases. In general, the deformation diagram of the wrinkled film/substrate system can be divided into three regions, i.e., the change of surface wrinkle amplitude, the irregular wrinkling, and the secondary wrinkling, governed by the four parameters above. Parallel finite element method (FEM) simulations are carried out which have good agreement with the theoretical predictions. The findings may be useful to guide the design and performance of stretchable electronics, cosmetic products, biomedical engineering, soft materials, and devices.

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References

Figures

Grahic Jump Location
Fig. 1

Schematic illustrations of the surface wrinkle modulation due to eigenstrain in the film. First, a film is adhered to the wrinkled compliant substrate (a), and then a contraction strain is induced in the film (b). Due to the contraction strain in the film, the amplitude of the wrinkles decreases from A to A1 (c).

Grahic Jump Location
Fig. 2

The relations of the membrane strain (solid line) and membrane stress (dashed line) to the applied eigenstrain in the film. The marked point corresponds to the critical buckling stress σ1* and eigenstrain εcom*. Secondary buckling may occur for εcom>εcom*. Here, the ratio of the plane strain modulus between the film and the substrate is E¯f/E¯s=50, film thickness to wavelength ratio h/λ = 0.025, and initial wrinkle amplitude to wavelength ratio A/λ = 0.05.

Grahic Jump Location
Fig. 3

The evolution of the surface wrinkles as the eigenstrain induced in the film. (a) The deformed configurations of the wrinkled film/substrate system for the contraction eigenstrain from εcom=0 to εcom=−0.1 and (b) for the expansion eigenstrain from εcom=0 to εcom=0.1, where E¯f/E¯s=300, h = 0.5 mm, λ = 10 mm, and A = 0.5 mm. The color contour represents the distribution of ε1.

Grahic Jump Location
Fig. 4

The relations between the relative change of the wrinkle amplitude to the applied eigenstrain in the film for three sets of parameters, i.e., E¯f/E¯s=300, A/λ = 0.025; E¯f/E¯s=300, A/λ = 0.05; and E¯f/E¯s=10, A/λ = 0.05, respectively. The solid lines are the theoretical predictions from Eq. (11), and the scattered stars are the FEM simulation results. Here, the wrinkle wavelength is 10 mm, and the film thickness is 0.5 mm for all of the three cases.

Grahic Jump Location
Fig. 5

Comparison of the relations of the wrinkle amplitude change to plane strain modulus ratio between theoretical predictions (Eq. (11)) and FEM simulations with h/λ = 0.05, A/λ = 0.05 (a) and h/λ = 0.05, A/λ = 0.025 (b), respectively. (c) and (d) Comparison of the relations of the wrinkle amplitude change to the film thickness h/λ with E¯f/E¯s  = 50, A/λ = 0.05 and E¯f/E¯s  = 50, A/λ = 0.025, respectively. (e) and (f) Comparison of the relations of the wrinkle amplitude change to the initial wrinkle amplitude A/λ with E¯f/E¯s  = 300, h/λ = 0.025 and E¯f/E¯s  = 100, h/λ = 0.025, respectively. Note that the negative value of ΔA/A corresponds to the contraction eigenstrain in the film, while the positive value of ΔA/A corresponds to the expansion eigenstrain.

Grahic Jump Location
Fig. 6

(a) The evolution of the surface wrinkles of the wrinkled film/substrate system under expansion eigenstrain in the film. (b) The relation between the strain energy of the film and the eigenstrain. A bifurcation point is defined as the zero value of the second derivative of the strain energy–eigenstrain curve which is indicated in the upper left corner. (c) The membrane strain in the film from theoretical prediction (solid line) and FEM simulation (dashed line). The two lines are deviated from each other after the bifurcation point. Here, the plane strainmodulus ratio is E¯f/E¯s  = 40, wrinkle wavelength λ = 20 mm, film thickness h = 0.5 mm, and initial wrinkle amplitude A = 0.5 mm.

Grahic Jump Location
Fig. 7

The relation of the critical eigenstrain εcom* to the plane strain modulus ratio obtained from theoretical analysis (solid line) and FEM simulations (square symbols). The dashed line is also the theoretical prediction of the critical eigenstrain εcom* from Eq. (15). Here, the film thickness, the wrinkle wavelength, and the initial wrinkle amplitude are the same as that in Fig. 6.

Grahic Jump Location
Fig. 8

Phase diagram of the deformation patterns of the wrinkled film/substrate system. There are three types of surface morphology, i.e., the change of surface wrinkle amplitude (I), the irregular wrinkling (II), and the secondary wrinkling (III).

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