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Continuum theory
for mechanical metamaterials with a cubic lattice
substructure
Simon R. Eugster, Francesco dell’Isola and David J. Steigmann
Vol. 7 (2019), No. 1, 75–98
DOI: 10.2140/memocs.2019.7.75
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Abstract |
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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. |
Keywords
mechanical metamaterials, Cosserat elasticity,
strain-gradient theory
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Mathematical Subject Classification 2010
Primary: 74A05, 74A30, 74A60, 74B20
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Milestones
Received: 5 February 2019
Revised: 13 February 2019
Accepted: 2 March 2019
Published: 22 April 2019
Communicated by Holm Altenbach
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Authors |
| Simon R. Eugster | |
| Institute for Nonlinear
Mechanics Universität Stuttgart Stuttgart Germany |
International Centre for Mathematics
and Mechanics of Complex Systems Università dell’Aquila L’Aquila Italy |
| Francesco dell’Isola | |
| Dipartimento di Ingegneria
Strutturale e Geotecnica Università di Roma “La Sapienza” Roma Italy |
International Centre for Mathematics
and Mechanics of Complex Systems Università dell’Aquila L’Aquila Italy |
| David J. Steigmann | |
| Department of Mechanical
Engineering University of California, Berkeley Berkeley, CA United States |
International Centre for Mathematics
and Mechanics of Complex Systems Università dell’Aquila L’Aquila Italy |
