Analytic analysis of auxetic metamaterials through analogy with rigid link systems

In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic r...

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Published inProceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 474; no. 2210; p. 20170753
Main Authors Rayneau-Kirkhope, Daniel, Zhang, Chengzhao, Theran, Louis, Dias, Marcelo A.
Format Journal Article
LanguageEnglish
Published England The Royal Society Publishing 01.02.2018
EditionRoyal Society (Great Britain)
Subjects
Auxetic
Buckling
Elastic instability
Elastic properties
Finite element method
Lattices
Mechanical Metamaterials
Mechanical properties
Metamaterials
Post-Buckling
Postbuckling
Stability analysis
post-buckling
auxetic
mechanical metamaterials
lattices
Online AccessGet full text
ISSN1364-5021
1471-2946
DOI10.1098/rspa.2017.0753

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Abstract In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite-element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson’s ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling-induced auxetic metamaterials.
AbstractList In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite-element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson’s ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling-induced auxetic metamaterials.
In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite-element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson's ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling-induced auxetic metamaterials.In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value. This paper develops a novel methodology in the analysis of auxetic metamaterials which exhibit elastic instability through analogy with rigid link lattice systems. The results of our analytic approach are confirmed by finite-element simulations for both the onset of elastic instability and post-buckling behaviour including Poisson's ratio. The method gives insight into the relationships between mechanisms within lattices and their mechanical behaviour; as such, it has the potential to allow existing knowledge of rigid link lattices with auxetic paths to be used in the design of future buckling-induced auxetic metamaterials.
Author Theran, Louis
Zhang, Chengzhao
Dias, Marcelo A.
Rayneau-Kirkhope, Daniel
AuthorAffiliation 4 School of Mathematics and Statistics , University of St Andrews , St Andrews KY16 9SS, Scotland, UK
2 Aalto Science Institute, Aalto University , 02150 Espoo, Finland
1 Department of Applied Physics, Aalto University , 02150 Espoo, Finland
3 Department of Mathematics , Massachusetts Institute of Technology , Cambridge, MA, USA
5 Department of Engineering , Aarhus University , Inge Lehmanns Gade 10, 8000 Aarhus C, Denmark
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Keywords post-buckling
auxetic
mechanical metamaterials
lattices
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Snippet In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is...
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SubjectTerms Auxetic
Buckling
Elastic instability
Elastic properties
Finite element method
Lattices
Mechanical Metamaterials
Mechanical properties
Metamaterials
Post-Buckling
Postbuckling
Stability analysis
Title Analytic analysis of auxetic metamaterials through analogy with rigid link systems
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