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Elastic buckling of gradient thin films on compliant substrates

Spontaneous buckling of films with either a thickness gradient or a material gradient offers a new opportunity for creating a variety of non-uniform undulating surface features with wide potential applications. The fundamental buckling mechanisms are explored both numerically and analytically in this article. When the loading direction is perpendicular to the gradient direction, Y-branched wrinkled channels are formed. When the load is parallel to the gradient direction, a transition from local to global buckle is observed as the load increases, and the resulting wavelength and amplitude are non-uniform in the loading direction. An analytical model is established which can effectively predict the buckling characteristics.