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Controlled wrinkling analysis of thin films on gradient substrates

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Abstract

The paper investigates continuously changing wrinkle patterns of thin films bonded to a gradient substrate. Three types of gradient substrates including exponential, power-law, and symmetry models are considered. The Galerkin method is used to discretize the governing equation of film bonded to gradient substrates. The wavelength and the normalized amplitude of the wrinkles for substrates of various material gradients are obtained. The numerical simulation based on the finite element method (FEM) is used to evolve the wrinkle patterns. The result agrees well with that of the analytical model. It is concluded that localization of wrinkle patterns strongly depends on the material gradient. The critical membrane force depends on both the minimum value of wrinkle stiffness and the gradient of wrinkle stiffness when the wrinkle stiffness is at its minimum. This work provides a better understanding for local wrinkle formation caused by gradient substrates.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China

    Jianzhong Zhao, Xingming Guo & Lu Lu

Authors
  1. Jianzhong Zhao
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  2. Xingming Guo
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  3. Lu Lu
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Corresponding author

Correspondence to Xingming Guo.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11472163), the National Key Basic Research Project of China (No. 2014CB04623), and the Shanghai Municipal Commission of Eduction (No. 13ZZ067)

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Zhao, J., Guo, X. & Lu, L. Controlled wrinkling analysis of thin films on gradient substrates. Appl. Math. Mech.-Engl. Ed. 38, 617–624 (2017). https://doi.org/10.1007/s10483-017-2199-9

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  • DOI: https://doi.org/10.1007/s10483-017-2199-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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