Curvature, metric and parametrization of origami tessellations: Theory and application to the eggbox pattern

Hussein Nassar; Arthur Lebée; Laurent Monasse

doi:10.1098/rspa.2016.0705

Curvature, metric and parametrization of origami tessellations: Theory and application to the eggbox pattern

Hussein Nassar ^{1, 2} Arthur Lebée ¹ Laurent Monasse ²

2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

Abstract : Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of non-linear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.

Keywords : Origami Metasurface Form finding Floppy modes Eggbox

Document type :

Journal articles

Domain :

Engineering Sciences [physics] / Mechanics [physics.med-ph]

Mathematics [math] / Differential Geometry [math.DG]

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https://hal.archives-ouvertes.fr/hal-01368009
Contributor : Hussein Nassar <>
Submitted on : Sunday, September 18, 2016 - 6:58:46 PM
Last modification on : Monday, April 15, 2019 - 6:08:01 PM

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