Rate-dependent wrinkling and subsequent bifurcations of an elastic thin film on a viscoelastic layer

A trilayer model with a viscoelastic layer between an elastic thin film and a pre-stretched elastomer substrate is used to study the rate-dependent wrinkling and subsequent bifurcations, where the elastic film and the visco-elastic layer are compressed by releasing the pre-stretch of the substrate at a prescribed nominal strain rate. With a moderate substrate pre-stretch, the only bifurcation mode obtained is wrinkling, with evolution of wrinkle wavelength and amplitude depending on the strain rate and the thickness of the viscoelastic layer. With a relatively large pre-stretch, the wrinkles may evolve to advanced bifurcation modes. Localized ridge formation occurs when the strain rate is low and the viscoelastic layer is thin. In contrast, when the strain rate is relatively high and the viscoelastic layer is thick, period-doubling occurs after a critical strain, which may further evolve to period quadrupling and periodic folding by consecutive bifurcations. By varying the substrate pre-stretch and the thickness ratio, bifurcation phase diagrams at the end of compression are constructed for different nominal strain rates. After compression, holding the trilayer at a constant nominal strain allows the surface morphology to evolve over time, eventually reaching an equilibrium state independent of the strain rate. The equilibrium bifurcation phase diagram obtained after holding shows three bifurcation modes: wrinkling, ridge formation, and periodic folding. Compared to the elastic bilayer systems, the trilayer system with a viscoelastic mid-layer offers additional control parameters in terms of the nominal strain rate and the thickness ratio to induce various bifurcation modes, which may enable designing and producing desired features of surface morphology for novel applications.