Compression-induced buckling of thin films bonded to viscous substrates: Uniform wrinkles vs localized ridges

Abstract

We examine the buckling of a thin elastic film bonded to a much thicker viscous substrate undergoing compression at a fixed rate. Experiments show two distinct buckling modes. At high rate of compression or at large liquid thickness, the buckles take on the form of approximately-sinusoidal wrinkles. At low rate of compression or at small liquid thickness, the buckles are highly localized into tall ridges separated nearly flat regions. Ridge growth is accompanied by lateral motion of the film in the near-ridge region, and the liquid in that region undergoes severe shear flow. Such ridge formation is entirely distinct from other examples of curvature localization such as fold localization of films on liquids in static equilibrium or ridge formation of films bonded to hyperelastic substrates. We quantify how the two lengthscales that arise from the buckling process, the wrinkle amplitude and the interridge distance, depend on compression rate and liquid thickness. We show that wrinkles formed during compression can also transform into ridges under quiescent conditions which suggests that buckle localization reduces bending energy of the film. We speculate that ridge localization appears due to a competition between two effects: a buckle mode with a few well-spaced ridges offers a lower energy state than uniform wrinkles, but wrinkles can develop faster because they require the viscous fluid to move over shorter distances.