Buckling of two-layer thin films embedded in compliant substrates

In this study, we investigate the buckling of a two-layer stiff film embedded in compliant substrates under uniaxial compression and derive the corresponding analytical solution. The theoretical predictions are validated through finite element simulations. We analyze the influence of the thickness and material parameters of the substrate and film on the critical buckling. This work contributes to a deeper understanding of buckling problems in industrial engineering and the morphological changes of biological tissues in nature. Furthermore, by setting special material parameters to the substrate, the present theoretical model can also be applied to address the buckling issue of a single-layer thin film bonded to the substrate surface as well as to solve the buckling problem of thin films bonded to both surfaces of a single-layer flexible substrate.