Stress-driven buckling patterns in spheroidal core/shell structures

Jie YIN, Zexian CAO, Chaorong LI, Izhak SHEINMAN, Xi CHEN*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

202 Citations (Scopus)


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. © 2008 by The National Academy of Sciences of the USA.
Original languageEnglish
Pages (from-to)19132-19135
Number of pages4
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number49
Publication statusPublished - 9 Dec 2008
Externally publishedYes

Bibliographical note

Acknowledgments: This work was supported by National Science Foundation Grant CMMI-CAREER-0643726, National Science Foundation of China Grants 60621091 and 50772100, and the Civil Space Exploration Program of China.


  • Morphogenesis
  • Nonlinear mechanics
  • Pattern formation
  • Physical geometry


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