Jump to main content
Jump to site search
Access to RSC content Close the message box

Continue to access RSC content when you are not at your institution. Follow our step-by-step guide.


Issue 41, 2018
Previous Article Next Article

Growth of form in thin elastic structures

Author affiliations

Abstract

Heterogeneous growth plays an important role in the shape and pattern formation of thin elastic structures ranging from the petals of blooming lilies to the cell walls of growing bacteria. Here we address the stability and regulation of such growth, which we modeled as a quasi-static time evolution of a metric, with fast elastic relaxation of the shape. We consider regulation via coupling of the growth law, defined by the time derivative of the target metric, to purely local properties of the shape, such as the local curvature and stress. For cylindrical shells, motivated by rod-like E. coli, we show that coupling to curvature alone is generically linearly unstable to small wavelength fluctuations and that additionally coupling to stress can stabilize these modes. Interestingly, within this framework, the longest wavelength fluctuations can only be stabilized with the mean curvature flow. Our approach can readily be extended to gain insights into the general classes of stable growth laws for different target geometries.

Graphical abstract: Growth of form in thin elastic structures

Back to tab navigation

Supplementary files

Article information


Submitted
01 Jun 2018
Accepted
18 Sep 2018
First published
18 Sep 2018

Soft Matter, 2018,14, 8361-8371
Article type
Paper
Author version available

Growth of form in thin elastic structures

S. Al Mosleh, A. Gopinathan and C. Santangelo, Soft Matter, 2018, 14, 8361
DOI: 10.1039/C8SM01136B

Social activity

Search articles by author

Spotlight

Advertisements