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Research Papers

Mechanism of Three-Dimensional Surface Wrinkle Manipulation on a Compliant Substrate

[+] Author and Article Information
Mengjie Li, Huasong Qin, Jingran Liu

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China;
Shaanxi Engineering Research Center of
Nondestructive Testing and Structural
Integrity Evaluation,
Xi'an Jiaotong University,
Xi'an 710049, China

Yilun Liu

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China;
Shaanxi Engineering Research Center of
Nondestructive Testing and Structural
Integrity Evaluation,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: yilunliu@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 16, 2018; final manuscript received April 6, 2018; published online May 8, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(7), 071004 (May 08, 2018) (11 pages) Paper No: JAM-18-1034; doi: 10.1115/1.4039951 History: Received January 16, 2018; Revised April 06, 2018

In this work, the surface wrinkle modulation mechanism of the three-dimensional (3D) film/substrate system caused by biaxial eigenstrains in the films is studied. A theoretical model based on the energy minimization of the 3D wrinkled film/substrate system is proposed which shows that the change of the surface wrinkle amplitude is determined by four dimensionless parameters, i.e., the eigenstrain in the film, plane strain modulus ratio between the film and substrate, film thickness to wrinkle wavelength ratio, and initial wrinkle amplitude to wavelength ratio. The surface wrinkle amplitude decreases (even almost flat) upon contraction eigenstrain in the film, while increases for that of expansion eigenstrain. Parallel finite element method (FEM) simulations are carried out which have good agreements with the theoretical predictions, and experimental verifications are also presented to verify the findings. Besides, different patterns of 3D surface wrinkles are studied and the similar surface wrinkle modulation is also observed. The findings presented herein may shed useful insights for the design of complex stretchable electronics, cosmetic products, soft devices and the fabrication of 3D complex structures.

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Figures

Grahic Jump Location
Fig. 1

Schematic illustrations of 3D surface wrinkle modulation due to the eigenstrain in the film. First, a film is adhered to the wrinkled substrate (film adhesion) (a), and then, a contraction strain is induced in the film (film contraction) (b). Due to the contraction strain in the film, the amplitude of the wrinkles decreases from A to A1 (wrinkles smoothing) (c).

Grahic Jump Location
Fig. 2

The evolution of surface wrinkles for different eigenstrains in the film. (a) The deformed configurations of the wrinkled film/substrate system at contraction eigenstrain from εcom = 0 to εcom = −0.1 and (b) at expansion eigenstrain from εcom = 0 to εcom = 0.1, where E¯f/E¯s=300, h = 0.5 mm, λ = 20.0 mm, and A = 1.0 mm.

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Fig. 3

The relations between the relative change of the wrinkle amplitude to the applied eigenstrain in the film for four sets of parameters, i.e., (a) E¯f/E¯s=100, A/λ = 0.05, h/λ = 0.025 and E¯f/E¯s=10, A/λ = 0.05, h/λ = 0.025; (b) E¯f/E¯s=100, A/λ = 0.05, h/λ = 0.025 and E¯f/E¯s=100, A/λ = 0.01, h/λ = 0.025; (c) E¯f/E¯s=100, A/λ = 0.05, h/λ = 0.05; and (d) h/λ = 0.025, A/λ = 0.025, E¯f/E¯s=100, respectively. The solid lines are the theoretical predictions from Eq. (12) and the symbols are the FEM simulation results.

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Fig. 4

Comparison of the relative wrinkle amplitude change between theoretical predictions (Eq. (12)) and FEM simulations. (a) The relations of the wrinkle amplitude change to the plane modulus ratio for h/λ = 0.025 and A/λ = 0.05; (b) the relations of the wrinkle amplitude change to the film thickness h/λ for E¯f/E¯s = 100 and A/λ = 0.05; and (c) the relations of the wrinkle amplitude change to the initial wrinkle amplitude A/λ for E¯f/E¯s = 100 and h/λ = 0.025. 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.

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Fig. 5

Three wrinkle patterns described by Eq. (13): (a) Checkboard mode for B = 0 and q = 1, (b) Parallel bead-chain mode for p = 1 and q = 3, and (c) Hexagonal mode for p = 2 and q = 3

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Fig. 6

The FEM simulation results of the wrinkle modulation for parallel bead-chain mode. (a) The evolution of the wrinkle amplitude under contraction eigenstrain in the film for E¯f/E¯s=300, A/λ = 0.025, and h/λ = 0.025. (b) The relation of the wrinkle amplitude change to the plane modulus ratio for A/λ = 0.025, h/λ = 0.025, and εcom = −0.1. (c) The relation of wrinkle amplitude change to h/λ for E¯f/E¯s=100, A/λ = 0.025, and εcom = −0.1. (d) The relation of wrinkle amplitude change to A/λ for h/λ = 0.025, E¯f/E¯s=100, and εcom = −0.1.

Grahic Jump Location
Fig. 7

The FEM simulation results of the wrinkle modulation for hexagonal mode. (a) The evolution of the wrinkle amplitude under contraction eigenstrain in the film for E¯f/E¯s=300, A/λ = 0.05, and h/λ = 0.025. (b) The relation of the wrinkle amplitude change to the plane modulus ratio for A/λ = 0.05, h/λ = 0.025, and εcom = −0.1. (c) The relation of wrinkle amplitude change to h/λ for E¯f/E¯s=100, A/λ = 0.05, and εcom = −0.1. (d) The relation of wrinkle amplitude change to A/λ for h/λ = 0.025, E¯f/E¯s=100, and εcom = −0.1.

Grahic Jump Location
Fig. 8

(a) The relation between the contraction strain and temperature for thermal shrinkage of the PVC film. (b) The configurations of the PVC film before and after thermal shrinkage at temperature 80 °C. (c) The stress–strain curve of the PVC film under uniaxial tensile test and (d) the stress–strain curve of the compliant substrate. The insets in (c) and (d) are the experimental photographs of the film and substrate.

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Fig. 9

The diagrams of the experiment procedure. (a) A wrinkled compliant substrate is first fabricated by casting and curing of the silicone liquid. (b) The PVC film is adhered to the wrinkled substrate. (c) The configuration of the wrinkled film-substrate system before thermal shrinkage of the PVC film and (d) the configuration after placing in a draught drying cabinet at temperature 80 °C for 10 min.

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Fig. 10

The surface heights of the wrinkled film/substrate system before and after thermal shrinkage of the PVC film for A/λ = 0.1 (a), A/λ = 0.075 (b), A/λ = 0.05 (c), and A/λ = 0.025 (d), respectively. The dashed and solid lines represent the height of the wrinkled surface before and after thermal shrinkage, respectively. Here, the wrinkle pattern is the checkboard mode with wavelength λ = 10 mm.

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Fig. 11

The relations of the wrinkle amplitude change ΔA/A to A/λ from experiments (circles) and theoretical predictions (squares). Here, the plane modulus ratio and the thickness to wavelength ratio are E¯f/E¯s=40,000 and h/λ = 0.005, respectively.

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