Surface wrinkling of nanostructured thin films on a compliant substrate

The wrinkling of films on a soft substrate is a critical issue of many technologically important applications and thus has attracted considerable attentions. However, the effect of the surface roughness on the buckling mode of the film remains unclear. In the present paper, the buckling of a rough film, resting on a compliant substrate is theoretically investigated. Dimensional analysis and large-scale finite element computations are performed to explore the wrinkling behavior of a film with periodically triangular or sinusoidal nanostructured (rough) surface patterns. The dependence relationship of the wrinkling wavelength on the geometric parameters of surface nanostructures and the elastic properties of the film and substrate is established. Our study shows that the effects of various surface nanostructures on the film buckling can be well described by using the concept of the equivalent thickness. A relation between the equivalent thickness and the geometric parameters of the system are derived by fitting our computational results. The results reported here may be instructive for surface patterning and biomimetic design of novel materials and devices with specific surface properties. To demonstrate the potential application of the buckling method in the fabrication of hierarchical surface structures, we provide two examples inspired by the micro/nano-patterns on lotus leaves and mosquito legs.