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Analytical study of wrinkling in thin-film-on-elastomer system with finite substrate thickness

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Abstract

Surface wrinkling, a film bonded on a pre-strained elastomeric substrate can form periodic wrinkling patterns, is a common phenomenon in daily life. In existing theoretical models, the film is much thinner than the substrate so that the substrate can be considered to be elastomeric with infinite thickness. In this paper, the effect of finite substrate thickness is analyzed theoretically for free boundary condition cases. Based on the minimum potential energy principle, a theoretical model is established, and the wave length and amplitude of the wrinkling pattern are obtained. When the thickness of the substrate is more than 200 times larger than the thickness of the film, the results of this study agree well with the results obtained from the previous models for infinite substrate thickness. However, for thin substrates, the effect of finite substrate thickness becomes significant. The model given in this paper accurately describes the effect of finite substrate thickness, providing important design guidelines for future thin-film-on-substrate systems such as stretchable electronic devices.

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Authors and Affiliations

  1. School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China

    Xianhong Meng, Guanyu Liu & Zihao Wang

  2. School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK, 74078, USA

    Shuodao Wang

Authors
  1. Xianhong Meng
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  2. Guanyu Liu
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  3. Zihao Wang
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  4. Shuodao Wang
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Corresponding author

Correspondence to Xianhong Meng.

Additional information

Project supported by the National Natural Science Foundation of China (Nos.11572022 and 11172022)

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Meng, X., Liu, G., Wang, Z. et al. Analytical study of wrinkling in thin-film-on-elastomer system with finite substrate thickness. Appl. Math. Mech.-Engl. Ed. 38, 469–478 (2017). https://doi.org/10.1007/s10483-017-2189-6

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  • DOI: https://doi.org/10.1007/s10483-017-2189-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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