Direct numerical simulations of three-dimensional surface instability patterns in thin film-compliant substrate structures.

A comprehensive numerical study of three-dimensional surface instability patterns is presented. The formation of wrinkles is a consequence of deformation instability when a thin film, bonded to a compliant substrate, is subject to in-plane compressive loading. We apply a recently developed computational approach to directly simulate complex surface wrinkling from pre-instability to post-instability in a straightforward manner, covering the entire biaxial loading spectrum from pure uniaxial to pure equi-biaxial compression. The simulations use embedded imperfections with perturbed material properties at the film-substrate interface. This approach not only triggers the first bifurcation mode but also activates subsequent post-buckling states, thus capable of predicting the temporal evolution of wrinkle patterns in one simulation run. The state of biaxiality is found to influence the surface pattern significantly, and each bifurcation mode can be traced back to certain abrupt changes in the overall load-displacement response. Our systematic study reveals how the loading condition dictates the formation of various instability modes including one-dimensional (1D) sinusoidal wrinkles, herringbone, labyrinth, and checkerboard.