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Continuum theory for mechanical metamaterials with a cubic lattice substructure

Abstract : A three-dimensional continuum theory for fibrous mechanical metamaterials is proposed, in which the fibers are assumed to be spatial Kirchhoff rods whose mechanical response is controlled by a deformation field and a rotation field, the former accounting for strain of the rod and the latter for flexure and twist of the rod as it deforms. This leads naturally to a model based on Cosserat elasticity. Rigidity constraints are introduced that effectively reduce the model to a variant of second-gradient elasticity theory.
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Submitted on : Friday, August 23, 2019 - 12:02:19 PM
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Simon R. Eugster, Francesco Dell'Isola, David Steigmann. Continuum theory for mechanical metamaterials with a cubic lattice substructure. Mathematics and Mechanics of Complex Systems, mdp, 2019, 7 (1), pp.75-98. ⟨10.2140/memocs.2019.7.75⟩. ⟨hal-02269803⟩



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