Theoretical predictions and evolutions of wrinkles in the film-intermediate layer-substrate structure under compression. (15th August 2022) - Wang, Bo; Zhang, Bohan; Bi, Haohao; Ouyang, Huajiang; Huang, Yongan; Wang, Shuodao
Abstract: The strategy of tuning the applied compressive strain on the stiff film/intermediate layer /soft substrate structure (named as the tri-layer structure), which can generate different kinds of surface wrinkling patterns, has been successfully utilized to fabricate stretchable electronic devices. In this paper, theoretical predictions and evolutions of wrinkles in the tri-layer structure have been done. Firstly, the theoretical model of the tri-layer structure is established, which takes the deformation of the intermediate layer into account due to the interfacial shear stress between the film and the intermediate layer. Secondly, the energy method is adopted and the analytical expressions of the critical strain and wavelength of the wrinkles in equilibrium are formulized, based on the principle of minimum potential energy. Then, through the wrinkling analysis, the correctness and superiority of the proposed formulations are verified; the unified theoretical formulations in this paper can be used to predict the first-order wrinkling patterns. Finally, by using the unified theoretical formulations, the evolution from a first-order wrinkling pattern to a second-order wrinkling pattern is first theoretically predicted in this paper. Through the post-buckling analysis, it is found that the second-order wrinkling patterns can be seen as the nested-first-order wrinkling patterns.