Buckling patterns of conical thin film/substrate systems

Mechanical buckling principles of conical film/substrate systems are explored in this study using extensive finite element simulations. The effects of geometrical and material parameters, including cone angle, normalized cone size, film/substrate thickness ratio, and modulus ratio between film and substrate, are explored systematically in terms of the resulting stress anisotropy (in particular the ratio between hoop and longitudinal stresses) and buckling morphology (longitudinal ridges, latitudinal stripes and reticular/herringbone patterns, as well as their transition and branching behaviours). The trends of buckling shape and wave numbers are also explored through analytical solutions of similar hollow cylindrical film/substrate systems. Finally, the mechanical buckling principles are employed to reproduce the morphological features of several types of mollusks, where each distinctive appearance corresponds to certain ranges of material and geometrical parameters. In addition to shedding some light on the morphogenesis of certain natural and biological systems, the study may also provide some useful insights on biomedical engineering and three-dimensional micro-fabrications. (paper)