Post-buckling evolution of wavy patterns in trapezoidal film/substrate bilayers

This paper investigates quantitatively the post-buckling response of irregular wrinkles in a trapezoidal film/substrate bilayer. The geometric gradient can change the wrinkling profile to create ribbed and graded structural patterns with variations of wave direction, amplitude and wavelength. The tapered angle and edge dimension are examined numerically using a nonlinear shell/solid coupled finite element model that incorporates a path-following continuation technique, which explores their influences on secondary bifurcations, localization and surface mode transition. For instance, the competition between plate-like and beam-like post-buckling behavior is discussed. An analysis of graded amplitude is also provided based on Fourier envelope equations of beam/foundation models, which gives an insightful understanding of these fading wrinkles that differ from the ones usually observed in rectangular geometric cases. The results of this work can be used to guide the design of geometrically gradient film/substrate systems to achieve desired wavy instability patterns.