Rate-controlled buckling of elastic thin films bonded to viscous substrates: Slow compression gives localized ridges; fast compression gives wrinkles*

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 by nearly flat regions. 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 also quantify the large lateral motion of the film in the near-ridge region that accompanies ridge growth; this lateral motion implies severe shear flow in the liquid near the ridges. Simulations show 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.