Anisotropic buckling patterns in spheroidal film/substrate systems and their implications in some natural and biological systems |
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Authors: | Jie Yin Xi Chen Izhak Sheinman |
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Institution: | aDepartment of Earth and Environmental Engineering, Mail Code 4711, Columbia University, New York, NY 10027, USA;bFaculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel |
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Abstract: | We establish a quantitative mechanics framework of elastic buckling of a spheroidal thin film/substrate system, which is highly relevant to the morphologies of quite a few natural and biological systems. The anisotropic stress-driven bifurcation is governed by the ratios between the effective size/thickness, the equatorial/polar radii, and the substrate/film moduli. The possibilities of manipulating the undulations through external constraints, anisotropic growth/material properties, and substrate geometry/structure are discussed. Analytical equations correlating the undulation characteristics with the geometry/material properties are derived. The quantitative mechanics framework established herein not only has important implications on the morphogenesis of various fruits, vegetables, nuts, eggs, tissues, and animal body parts, but also could guide the three-dimensional micro-fabrications via controlled self-assembly on curved substrate surfaces. |
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Keywords: | Buckling Spheroid Thin film Morphogenesis |
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