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

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.