Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials

Kévin Billon (1) , Ioannis Zampetakis (2) , Fabrizio Scarpa (2) , Morvan Ouisse (1) , Emeline Sadoulet (1) , Manuel Collet (3) , Adam Perriman (4) , Alistair Hetherington (4)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 ACCIS - Advanced Composites Centre for Innovation and Science
3 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
4 University of Bristol [Bristol]

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.

Mots clés: Periodic structures; Metamaterial; Auxetic; Vibroacoustic

Domaines: Mécanique [physics]

Kévin Billon, Ioannis Zampetakis, Fabrizio Scarpa, Morvan Ouisse, Emeline Sadoulet, et al.. Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials. Composite Structures, 2017, 160, pp.1042-1050. ⟨10.1016/j.compstruct.2016.10.121⟩. ⟨hal-02131301⟩