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American Physical Society, Physical Review Letters, 6(105), 2010

DOI: 10.1103/physrevlett.105.068101

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Self-Contact and Instabilities in the Anisotropic Growth of Elastic Membranes

Journal article published in 2010 by Norbert Stoop, Martine Ben Amar, Falk K. Wittel, Hans J. Herrmann, Martin Michael Müller
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This paper is available in a repository.

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Abstract

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.