Wrinkling of a bilayer resting on a soft substrate under in-plane compression

Abstract

The wrinkling problem of a bilayer film resting on a soft substrate under in-plane compression is investigated via theoretical analysis and numerical simulations. Such a system may undergo two different wrinkling modes, namely surface wrinkling of the top single layer on a composite substrate or bilayer wrinkling on a homogeneous substrate, depending on the geometric and material parameters. In the present paper, a theoretical solution is first derived for the former case, while a solution available in the literature is applied for the latter. The solution derived here can degenerate both to the classical solution for a stiff layer resting on a semi-infinite soft substrate and that for a stiff layer lying on a compliant substrate of finite thickness. A series of finite element simulations are performed to demonstrate the accuracy of the theoretical solution. In addition, it is found that, at a given compressive strain, a certain change in the elastic modulus of the intermediate layer may lead to a dramatic surface pattern transformation between the two wrinkling modes, indicating a novel approach to realise surface pattern switching.

Keywords:

• wrinkling
• bilayer film
• soft substrate
• surface patterning
• pattern transformation

Acknowledgements

We thank Professor J.W. Hutchinson of Harvard University for his helpful suggestions on this work. Supports from the National Natural Science Foundation of China (Grant Nos. 10972112 and 10732050), Tsinghua University (2009THZ02122) and 973 Program (2010CB631005) are acknowledged.