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Journal Articles Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Year : 2017

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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Dates and versions

hal-01368009 , version 1 (18-09-2016)

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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, 2017, 473 (2197), ⟨10.1098/rspa.2016.0705⟩. ⟨hal-01368009⟩
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