Surface wrinkling of anisotropic films bonded on a compliant substrate

Material anisotropy regulates the instabilities of film-substrate systems at different length scale. In this paper, we investigate the surface wrinkling and morphological evolution of an orthotropic thin film resting on a compliant substrate. Under different loading conditions, the system may buckle into various surface patterns, e.g., stripe, checkerboard, and herringbone, which are analyzed by using the Föppl-von Kármán plate theory. The Fourier spectral method is employed to simulate the morphological evolutions of surface patterns under different loading biaxialities. We find that both loading biaxiality and material anisotropy affect the characteristics of surface wrinkling patterns and their evolutions. Stripe and checkerboard modes often emerge at the critical buckling and they tend to transform into herringbone and labyrinth patterns during postbuckling. Phase diagrams are established to reveal the dependence of surface patterns on material anisotropy, Poisson's effect, and loading biaxiality. This study may help design diverse functional surfaces and deepen our understanding of the morphogenesis of some soft biological tissues and organs.