Buckling of anisotropic films on cylindrical substrates: Insights for self-assembly fabrication of 3D helical gears

We propose an effective way of fabricating true three-dimensional helical gear-like structures (with inclined gear teeth) by using self-assembled stress-driven buckling of anisotropic films on compliant cylindrical substrates. Key parameters characterizing the helical undulation profile, in particular the gear teeth number and the inclined teeth angle, are investigated numerically using finite element simulations. Based on the insights from numerical calculations, a simplified theoretical model is established to effectively predict the teeth number. The results show that the anisotropic modulus ratio has a larger effect on the teeth number than the anisotropy angle. The orientation of gear teeth is related to the coupled effects of the anisotropic modulus ratio, anisotropy angle, substrate curvature and substrate aspect ratio. In general, the undulation orientation tends to be perpendicular to the direction of minimum bending stiffness in the film. The findings in this paper provide useful guidance for the self-assembly fabrication of helical gears and other 3D structures at various length scales. © 2010 IOP Publishing Ltd.