Anisotropic buckling patterns in spheroidal film/substrate systems and their implications in some natural and biological systems

Jie YIN, Xi CHEN, Izhak SHEINMAN

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

104 Citations (Scopus)

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. © 2009 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)1470-1484
Number of pages14
JournalJournal of the Mechanics and Physics of Solids
Volume57
Issue number9
DOIs
Publication statusPublished - 2009
Externally publishedYes

Bibliographical note

The study of this research was supported by NSFCMMI-CAREER-0643726. Experimental collaboration with Chaorong Li and Zexian Cao is acknowledged. The authors are benefited from valuable discussions with Professor John W. Hutchinson.

Keywords

  • Buckling
  • Morphogenesis
  • Spheroid
  • Thin film

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