Stress-driven buckling patterns in spheroidal core/shell structures

Fig. 2. Deformation map of a prolate spheroid with varying k and R/t (with E􏰐f/E􏰐s 􏰇 30). The black solid line separates the ribbed and reticular patterns.

From:
Jie Yin (1), Zexian Cao (2), Chaorong Li (3), Izhak Sheinman (1,4), Xi Chen (1)
(1) Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027-6699;
(2) Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China;
(3) Department of Physics and Key Laboratory of Advanced Textile Materials and Manufacturing Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China; and
(4) Faculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
“Stress-driven buckling patterns in spheroidal core/shell structures”, Proceedings of the National Academy of Sciences of the U.S.A., (PNAS), Vol. 105, No. 49, pp 19132-19135, October 20, 2008.
This article contains supporting information online at www.pnas.org/cgi/content/full/0810443105/DCSupplemental

ABSTRACT: Many natural fruits and vegetables adopt an approximately spheroidal shape and are characterized by their distinct undulating topologies. We demonstrate that various global pattern features can be reproduced by anisotropic stress-driven buckles on spheroidal core/shell systems, which implies that the relevant mechanical forces might provide a template underpinning the topological conformation in some fruits and plants. Three dimensionless parameters, the ratio of effective size/thickness, the ratio of equatorial/polar radii, and the ratio of core/shell moduli, primarily govern the initiation and formation of the patterns. A distinct morphological feature occurs only when these parameters fall within certain ranges: In a prolate spheroid, reticular buckles take over longitudinal ridged patterns when one or more parameters become large. Our results demonstrate that some universal features of fruit/vegetable patterns (e.g., those observed in Korean melons, silk gourds, ribbed pumpkins, striped cavern tomatoes, and cantaloupes, etc.) may be related to the spontaneous buckling from mechanical perspectives, although the more complex biological or biochemical processes are involved at deep levels.

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