The universal scaling law for wrinkle evolution in stiff membranes on soft films

•The effect of soft film thickness on the bifurcation of wrinkle instability is revealed •A scaling law can unify various bifurcations of wrinkle instability •A sample peeling method can precisely control wrinkle instability •Fracture based on buckling pattern sheds light on a new method for nanomanufacture Stiff membranes on soft substrates tend to wrinkle under compression. The evolution of post-wrinkle instability through wrinkling, period doubling to quadruple folds, and/or creases with increasing compression has been extensively studied, but how to control this intriguing evolution remains challenging. Here, we obtain a scaling law for wrinkle evolution in which a single parameter, consisting of thickness contrast of the soft film to the stiff membrane and a material constant, determines the final instability order of the wrinkle evolution. In sharp contrast to the common view that the thickness effect of the soft substrate is negligible as the thickness contrast reaches a few tens, the soft film thickness plays a dominant role for thickness contrast across several orders of magnitude. The law proves to be universal in a sufficiently large range of materials and geometries and thus should play a general role in controlling the complex behavior of natural and artificial stiff/soft bilayer systems. Stiff membranes on soft substrates tend to wrinkle under compression. The evolution of post-wrinkle instability through wrinkling, period doubling to quadruple folds, and/or creases with increasing compression has been extensively studied, but how to control this intriguing evolution remains challenging. Here, we obtain a scaling law for wrinkle evolution in which a single parameter, consisting of thickness contrast of the soft film to the stiff membrane and a material constant, determines the final instability order of the wrinkle evolution. In sharp contrast to the common view that the thickness effect of the soft substrate is negligible as the thickness contrast reaches a few tens, the soft film thickness plays a dominant role for thickness contrast across several orders of magnitude. The law proves to be universal in a sufficiently large range of materials and geometries and thus should play a general role in controlling the complex behavior of natural and artificial stiff/soft bilayer systems.