Transition behavior of buckling modes on a sphere

Feasibility of manipulating the thin film buckling patterns is investigated by changing the substrate curvature and the stress developed upon cooling. The numerical and experimental studies are based on the spherical SiO2 film/Ag substrate system. It is found that for a substrate with a relatively large curvature, the triangularly distributed dent-like buckling pattern forms when the nominal stress is just above a critical value. With increasing film stress and/or substrate radius, the labyrinth-like buckling patterns take over. Bothe the buckling wavelength and the critical buckling stress become larger with increasing substrate radius. Researches along this line are helpful to the understanding of the formation and evolution of many natural patterns including the phyllotactic arrangements and wrinkles.