%0 Journal Article %1 WOS:000280555000006 %A Stoop, Norbert %A Wittel, Falk K %A Amar, Martine Ben %A Mueller, Martin Michael %A Herrmann, Hans J %C ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA %D 2010 %I AMER PHYSICAL SOC %J PHYSICAL REVIEW LETTERS %K imported %N 6 %R 10.1103/PhysRevLett.105.068101 %T Self-Contact and Instabilities in the Anisotropic Growth of Elastic Membranes %V 105 %X 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.

@article{WOS:000280555000006, 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.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA}, author = {Stoop, Norbert and Wittel, Falk K and Amar, Martine Ben and Mueller, Martin Michael and Herrmann, Hans J}, biburl = {https://www.bibsonomy.org/bibtex/25abef723d3e861883139675d4ff14391/ppgfis_ufc_br}, doi = {10.1103/PhysRevLett.105.068101}, interhash = {57e501a51574815ba5e9ed9b7cf94546}, intrahash = {5abef723d3e861883139675d4ff14391}, issn = {0031-9007}, journal = {PHYSICAL REVIEW LETTERS}, keywords = {imported}, number = 6, publisher = {AMER PHYSICAL SOC}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Self-Contact and Instabilities in the Anisotropic Growth of Elastic Membranes}, tppubtype = {article}, volume = 105, year = 2010 }