A three-dimensional phase diagram of growth-induced surface instabilities
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Zhao_A three-dimensional.pdf
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1.14 MB
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Checksum (MD5)
4069a2d3921c6869e54e9a81b58ab23a
Author(s)
Wang, Qiming
Zhao, Xuanhe
Date Issued
March 2015
Journal
Scientific Reports
Publisher
Nature Publishing Group
Citation
Wang, Qiming, and Xuanhe Zhao. “A Three-Dimensional Phase Diagram of Growth-Induced Surface Instabilities.” Sci. Rep. 5 (March 9, 2015): 8887.
Version
Final published version
Abstract
A variety of fascinating morphological patterns arise on surfaces of growing, developing or aging tissues, organs and microorganism colonies. These patterns can be classified into creases, wrinkles, folds, period-doubles, ridges and delaminated-buckles according to their distinctive topographical characteristics. One universal mechanism for the pattern formation has been long believed to be the mismatch strains between biological layers with different expanding or shrinking rates, which induce mechanical instabilities. However, a general model that accounts for the formation and evolution of these various surface-instability patterns still does not exist. Here, we take biological structures at their current states as thermodynamic systems, treat each instability pattern as a thermodynamic phase, and construct a unified phase diagram that can quantitatively predict various types of growth-induced surface instabilities. We further validate the phase diagram with our experiments on surface instabilities induced by mismatch strains as well as the reported data on growth-induced instabilities in various biological systems. The predicted wavelengths and amplitudes of various instability patterns match well with our experimental data. It is expected that the unified phase diagram will not only advance the understanding of biological morphogenesis, but also significantly facilitate the design of new materials and structures by rationally harnessing surface instabilities.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1038/srep08887
