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A controlled surface wrinkling pattern has been widely used in diverseapplications, such as stretchable electronics, smart windows, and haptics.Here, we focus on hexagonal wrinkling patterns because of their greatpotentials in realizing anisotropic and tunable friction and serving as adynamical template for making non-flat thin films through self-assemblingprocesses. We employ large-scale finite element simulations of a bilayerneo-Hookean solid (e.g., a film bonded on a substrate) to explore mechanicalprinciples that govern the formation of hexagonal wrinkling patterns andstrategies for making nearly perfect hexagonal patterns. In our model, thewrinkling instabilities are driven by the confined film expansion. Our resultsindicate robust hexagonal patterns exist at a relatively small modulus mismatch(on the order of 10) between the film and substrate. Besides, the filmexpansion should not exceed the onset of wrinkling value too much to avoidpost-buckling patterns. By harnessing the imperfection insensitivity ofone-dimension sinusoidal wrinkles, we apply a sequential loading to the bilayerstructure to produce the nearly perfect hexagonal patterns. Lastly, we discussthe connection between the simple bilayer model and the gradient structurescommonly existed in experiments.

Understanding and controlling hexagonal patterns of wrinkles in neo-Hookean elastic bilayer structures