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

doi:10.1007/s10483-017-2189-6

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (4): 469-478.doi: https://doi.org/10.1007/s10483-017-2189-6

• 论文 • 下一篇

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

Xianhong MENG¹, Guanyu LIU¹, Zihao WANG¹, Shuodao WANG²

1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;
2. School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, U. S. A

收稿日期:2016-09-21 修回日期:2016-11-04 出版日期:2017-04-01 发布日期:2017-04-01
通讯作者: Xianhong MENG E-mail:mxh@buaa.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos.11572022 and 11172022)

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

Xianhong MENG¹, Guanyu LIU¹, Zihao WANG¹, Shuodao WANG²

1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;
2. School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, U. S. A

Received:2016-09-21 Revised:2016-11-04 Online:2017-04-01 Published:2017-04-01
Contact: Xianhong MENG E-mail:mxh@buaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.11572022 and 11172022)

摘要/Abstract

摘要：

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.

关键词: finite substrate thickness, wrinkling, theoretical mechanics model

Abstract:

Key words: finite substrate thickness, theoretical mechanics model, wrinkling

中图分类号:

O343.3

Xianhong MENG, Guanyu LIU, Zihao WANG, Shuodao WANG. Analytical study of wrinkling in thin-film-on-elastomer system with finite substrate thickness[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 469-478.

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

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

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