Quantized wrinkle and fracture of stiff membrane on soft film

Abstract

Abstract Stiff membranes on soft substrates tend to wrinkle under compression1–11. The evolution of post-wrinkle instability through wrinkling3,12, period doubling to quadruple folds, and/or creases4,9,11 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 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, thus, should play a general role in controlling the complex behavior of natural and artificial stiff/soft bilayer systems.