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Stress-driven buckling patterns in spheroidal core/shell structures

Yin, Jie, Cao, Zexian, Li, Chaorong, Sheinman, Izhak, Chen, Xi
Proceedings of the National Academy of Sciences of the United States of America 2008 v.105 no.49 pp. 19132-19135
biochemical pathways, cantaloupes, fruits, gourds, pumpkins, tomatoes
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.