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Article Dans Une Revue Extreme Mechanics Letters Année : 2022

Strain compatibility and gradient elasticity in morphing origami metamaterials

Hussein Nassar
Arthur Lebée

Résumé

The principles of origami design have proven useful in a number of technological applications. Origami tessellations in particular constitute a class of morphing metamaterials with unusual geometric and elastic properties. Although inextensible in principle, fine creases allow origami metamaterials to effectively deform non-isometrically. Determining the strains that are compatible with coarse-grained origami kinematics as well as the corresponding elasticity functionals is paramount to understanding and controlling the morphing paths of origami metamaterials. Here, within a unified theory, we solve this problem for a wide array of well-known origami tessellations including the Miura-ori as well as its more formidable oblique, non-developable and non-flat-foldable variants. We find that these patterns exhibit two universal properties. On one hand, they all admit equal but opposite in-plane and out-of-plane Poisson's ratios. On the other hand, their bending energy detaches from their in-plane strain and depends instead on the strain gradient. The results are illustrated over a case study of the self-equilibrium geometry of origami pillars.
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Dates et versions

hal-04390637 , version 1 (12-01-2024)

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Hussein Nassar, Arthur Lebée, Emily Werner. Strain compatibility and gradient elasticity in morphing origami metamaterials. Extreme Mechanics Letters, 2022, 53, pp.101722. ⟨10.1016/j.eml.2022.101722⟩. ⟨hal-04390637⟩
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