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

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.
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Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University Press (CUP), 2017, 473 (2197), 〈10.1098/rspa.2016.0705〉
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Soumis le : dimanche 18 septembre 2016 - 18:58:46
Dernière modification le : jeudi 18 janvier 2018 - 11:01:05

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Hussein Nassar, Arthur Lebée, Laurent Monasse. Curvature, metric and parametrization of origami tessellations: Theory and application to the eggbox pattern. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University Press (CUP), 2017, 473 (2197), 〈10.1098/rspa.2016.0705〉. 〈hal-01368009〉

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