Radial wrinkles on film–substrate system induced by local prestretch: A theoretical analysis

Abstract

Local wrinkles are widely observed in film–substrate systems both in nature and in engineering. In this paper, we investigate the surface wrinkling of a film–substrate structure subjected to local prestretch in a circular region. Hankel transform is used to unravel the interface condition between the stiff film and the compliant substrate. The critical prestrain and the corresponding wrinkling number are solved as functions of the radius of the prestretched region and the Young’s modulus ratio between the film and substrate. The theoretical analysis is validated by a semi-implicit numerical method based on the Fourier spectral technique. The postbuckling behavior is also simulated via the numerical method. It is found that during postbuckling, the surface wrinkles may experience a secondary bifurcation and evolve into branching patterns.