Buckling behaviour of a stiff thin film on a finite-thickness bi-layer substrate

In engineering stretchable electronics, an intermediate layer between a thin stiff film and a substrate can enhance the adhesion of the film and modulate its buckling shape. Capturing buckling behaviour of the tri-layer film/intermediate layer/substrate structure is essential for designing stretchable electronics. In this paper, considering the shear stress between the film and intermediate layer and using the complete mathematical form of the longitudinal displacement of the film, an improved theoretical model of the buckled tri-layer structure is established and the total energy of this tri-layer structure is derived. Based on the total energy, two buckling regimes, global (Euler) buckling and local wrinkling, influenced by the intermediate layer, are studied. Since local wrinkling is a desirable buckling pattern for stretchable electronics, accurate solutions of buckling wavelength and critical strain of local wrinkling verified by finite element analysis are determined. The influence of the intermediate layer on the wrinkling instability of the tri-layer structure is analysed. These results will aid in the design and manufacture of film/substrate-type stretchable electronics.