Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials

Kévin J Billon, Ioannis Zampetakis, Fabrizio Scarpa, Morvan Ouisse*, Emeline Sadoulet-Reboul, Manuel Collet, Adam Perriman, Alistair Hetherington

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

85 Citations (Scopus)
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We describe in this work a composite metamaterial with a hierarchical topology made by tessellating perforations that exhibit an auxetic (negative Poisson's ratio) behaviour. We perform an analysis of the hierarchical structure by evaluating the fractal order of the topologies associated to the perforated composites.The periodic hierarchical lattice configuration shows negative Poisson's ratio characteristics at higher levels of hierarchy, even when the baseline configuration has a topology not exhibiting an auxetic behaviour. We investigate the wave propagation characteristics of these particular hierarchical lattices by using a Bloch wave approach applied to detailed Finite Element geometries of the unit cell configurations. We show that the level of hierarchy creates new band gaps with large relative widths, and it also shifts the same bandgaps towards lower frequencies. We correlate the mechanical properties, fractal order and the dispersion characteristics of the multiscale auxetic perforated metamaterial with the parameters defining the geometry of the lattice and the hierarchy levels, and discuss the results in a nondimensional form to provide a performance map of the mechanical and dynamic properties.

Original languageEnglish
Pages (from-to)1042-1050
Number of pages9
JournalComposite Structures
Early online date1 Nov 2016
Publication statusPublished - 15 Jan 2017


  • Auxetic
  • Metamaterial
  • Periodic structures
  • Vibroacoustic


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