Analytic analysis of auxetic metamaterials through analogy with rigid link systems

Daniel Rayneau-Kirkhope*, Chengzhao Zhang, Louis Theran, Marcelo A. Dias

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Article number20170753
Pages (from-to)1-12
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2210
Publication statusPublished - 1 Feb 2018
MoE publication typeA1 Journal article-refereed


  • Auxetic
  • Lattices
  • Mechanical metamaterials
  • Post-buckling


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