Self-contact and instabilities in the anisotropic growth of elastic membranes

We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary t...

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Bibliographic Details
Published in:Physical review letters 2010-08, Vol.105 (6), p.068101-068101, Article 068101
Main Authors: Stoop, Norbert, Wittel, Falk K, Ben Amar, Martine, Müller, Martin Michael, Herrmann, Hans J
Format: Article
Language:English
Subjects:
Anisotropy
Elasticity
Imaging, Three-Dimensional
Membranes - growth & development
Models, Biological
Thermodynamics
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Summary:We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric e cone solution is energetically minimal any more. Instead, we obtain skewed e cone solutions having lower energy, characterized by a skewness angle and repetitive spiral winding with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.105.068101