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

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

2010-07-12

arxiv.org/abs/1007.1871v2

Phys. Rev. Lett. 105, 068101 (2010)

Physics

Biological Physics

4 pages, 5 figures; New version corresponds to the one published in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.105.068101

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 \textit{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.

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