Wrinkling pattern evolution on curved surfaces

We investigate the effects of surface curvature on the wrinkling pattern evolution in soft materials. Theoretical analysis and the Fourier spectral method are combined to understand the occurrence of surface wrinkling and pattern transitions. We reveal that surface curvature and its anisotropy play a key role in wrinkling pattern transitions, for example, from the sinusoidal to the hexagonal mode. Based on the nonlinear equilibrium equations, a Fourier spectral method is developed to track the surface wrinkling pattern evolution in a curved bilayer system. This method is validated by comparison between the simulation results and relevant experiments. The simulations show that a hexagonal phase may evolve into either a bistable or labyrinth phase, depending on the curvature anisotropy, the excess stress, a dimensionless curvature parameter, and the curvature gradient. This work can not only help understand the pattern formation in some natural systems, but the methods presented here can also find a broad range of technical applications, for examples, design of anticounterfeiting systems with high-security levels using labyrinth patterns on curved surfaces.