(518e) Buckling of Thin Elastic Films Under Viscous Stress

When a thin stiff film bonded to a compliant support is subjected to compressive stress, it buckles to form wrinkles. The situation when the compliant support is a soft elastic solid has been studied heavily. Here we examine the opposite extreme when the compliant support is a highly viscous liquid, and hence dissipates mechanical energy. In this situation, when the liquid is subjected to uniaxial compression, it transfers viscous stress to the film, which then buckles. The phenomenon is dependent on rate – not surprising given that the compliant support is viscous. We develop an approximate shear lag model to predict the evolution of the stress profile in the film prior to buckling. We show that the in-plane motion of the film can be described by a diffusion equation where the diffusivity is related to the fluid viscosity, film elasticity, and various lengthscales of the system. The evolution of the stress profile in the film is shown to depend on three quantities: the rate of compression, the thickness of the liquid layer, and the length of the elastic film, all suitably normalized by geometric and material parameters. A linear perturbation analysis is developed to predict the wavelength of wrinkles. Numerical simulations are conducted to predict nonlinear evolution of the wrinkle wavelength and amplitude. Experiments conducted using 25 micron thick elastic polymer films floating on a viscous polymer liquid show trends that are qualitatively consistent with the predictions. We also discuss observations of post-buckling “fold” formation in which roughly-sinusoidal wrinkles transition into more sharply curved features.