Vol. 7, No. 1, 2019

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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
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.

Keywords
mechanical metamaterials, Cosserat elasticity, strain-gradient theory
Mathematical Subject Classification 2010
Primary: 74A05, 74A30, 74A60, 74B20
Milestones
Received: 5 February 2019
Revised: 13 February 2019
Accepted: 2 March 2019
Published: 22 April 2019

Communicated by Holm Altenbach
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