Euclidean Frustrated Ribbons

Euclidean Frustrated Ribbons

Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. Previous research identified the origin of the frustration as the violation of Gauss’s Theorema Egregium. Such “Gauss frustration” exhibits rich phenomenology; it may lead t...

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Autores principales: Emmanuel Siéfert, Ido Levin, Eran Sharon
Formato: article
Lenguaje:EN
Publicado: American Physical Society 2021
Materias:
Physics
QC1-999
Acceso en línea:https://doaj.org/article/bedf504e288b4a249ba553f3ef6e448a
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spelling oai:doaj.org-article:bedf504e288b4a249ba553f3ef6e448a2021-12-02T17:09:30ZEuclidean Frustrated Ribbons10.1103/PhysRevX.11.0110622160-3308https://doaj.org/article/bedf504e288b4a249ba553f3ef6e448a2021-03-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.011062http://doi.org/10.1103/PhysRevX.11.011062https://doaj.org/toc/2160-3308Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. Previous research identified the origin of the frustration as the violation of Gauss’s Theorema Egregium. Such “Gauss frustration” exhibits rich phenomenology; it may lead to mechanical instabilities, anomalous mechanics, and shape-morphing abilities that can be harnessed in engineering systems. Here we report a new type of geometrical frustration, one that is as general as Gauss frustration. We show that its origin is the violation of Mainardi-Codazzi-Peterson compatibility equations and that it appears in Euclidean sheets. Combining experiments, simulations, and theory, we study the specific case of a Euclidean ribbon with radial and geodesic curvatures. Experiments, conducted using different materials and techniques, reveal shape transitions, symmetry breaking, and spontaneous stress focusing. These observations are quantitatively rationalized using analytic solutions and geometrical arguments. We expect this frustration to play a significant role in natural and engineering systems, specifically in slender 3D printed sheets.Emmanuel SiéfertIdo LevinEran SharonAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 1, p 011062 (2021)
institution DOAJ
collection DOAJ
language EN
topic Physics
QC1-999
spellingShingle Physics
QC1-999
Emmanuel Siéfert
Ido Levin
Eran Sharon
Euclidean Frustrated Ribbons
description Geometrical frustration in thin sheets is ubiquitous across scales in biology and becomes increasingly relevant in technology. Previous research identified the origin of the frustration as the violation of Gauss’s Theorema Egregium. Such “Gauss frustration” exhibits rich phenomenology; it may lead to mechanical instabilities, anomalous mechanics, and shape-morphing abilities that can be harnessed in engineering systems. Here we report a new type of geometrical frustration, one that is as general as Gauss frustration. We show that its origin is the violation of Mainardi-Codazzi-Peterson compatibility equations and that it appears in Euclidean sheets. Combining experiments, simulations, and theory, we study the specific case of a Euclidean ribbon with radial and geodesic curvatures. Experiments, conducted using different materials and techniques, reveal shape transitions, symmetry breaking, and spontaneous stress focusing. These observations are quantitatively rationalized using analytic solutions and geometrical arguments. We expect this frustration to play a significant role in natural and engineering systems, specifically in slender 3D printed sheets.
format article
author Emmanuel Siéfert
Ido Levin
Eran Sharon
author_facet Emmanuel Siéfert
Ido Levin
Eran Sharon
author_sort Emmanuel Siéfert
title Euclidean Frustrated Ribbons
title_short Euclidean Frustrated Ribbons
title_full Euclidean Frustrated Ribbons
title_fullStr Euclidean Frustrated Ribbons
title_full_unstemmed Euclidean Frustrated Ribbons
title_sort euclidean frustrated ribbons
publisher American Physical Society
publishDate 2021
url https://doaj.org/article/bedf504e288b4a249ba553f3ef6e448a
work_keys_str_mv AT emmanuelsiefert euclideanfrustratedribbons
AT idolevin euclideanfrustratedribbons
AT eransharon euclideanfrustratedribbons
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