Post-buckling behaviors of thin-film soft-substrate bilayers with finite-thickness substrate

Surface buckling behaviors of thin-film soft-substrate bilayers have important research value. Recent research has focused on bilayers with infinite-thickness substrates. However, bilayers with finite-thickness substrates widely exist. To study this problem more comprehensively, we extended the stability theory of a beam on an elastic foundation to bilayers and then established a finite element method of bilayers using the neo-Hookean hyperelastic constitutive model. A self-contact analysis method was coupled to the finite element method so that the further buckling evolution of the film surface after folding could be simulated. Based on our analysis of various modulus ratios and thickness ratios, the evolution of the buckling path was significantly influenced by the thickness ratio. Without considering the situation of a prestressed substrate, four new buckling paths were found. Thus, we extended the single buckling path (under infinite thickness substrate) to five types. Our study also found that for path four, the substrate with a certain thickness exhibited a special final stable surface morphology. That is, regardless of the friction, a new periodic morphology after film folding appeared due to the contact slip of the film surface. Finally, further analysis showed that these five buckling paths were all dependent on different modulus ratios and thickness ratios.