Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials

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

doi:10.1016/j.compstruct.2016.10.121

Abstract

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.

Highlights

Mechanical metamaterials have been recently hailed as a new class of structural concepts able to bring novel multifunctionalities [1] by changes of compliance,shapes, or by embedding oscillators or smart materials inserts
Negative Poisson’s ratio [11] is a mechanical feature of auxetic [12] or dilational [13] materials, and indicates an unusual large volumetric deformation that corresponds to a transverse dilatation with a uniaxial tensile loading
Auxetic structures and solids have been extensively evaluated for their mechanical wave propagation behaviour, because of their strong acoustic signature and potential phononic applications [14, 15, 16]

Summary

Introduction

Mechanical metamaterials have been recently hailed as a new class of structural concepts able to bring novel multifunctionalities [1] by changes of compliance,shapes, or by embedding oscillators or smart materials inserts. The presence of perforations with specific geometry and spacing in a planar continuum structure creates an in-plane negative Poisson’s ratio behaviour, whether one can use an elliptical [17] or rhomboidal architecture [18, 19]. The use of perforations is quite instrumental to create hierarchical configurations by tessellating in a self-similar way the perforated pattern and obtain auxetic configurations in planar and cylindrical domains [20]. Recent work has examined the use of cut hinges topologies in a hierarchical tessellation both from the static mechanical and in-plane wave propagation behaviour [29]. In this work we describe a configuration of hierarchical 2D metamaterial that is produced by a self-similar generation of a rectangular perforated topology with in-plane negative Poisson’s ratio ratio behaviour. The use of different hierarchical levels with fractal dimensions leads to tailoring and enlarging full and partial bandgaps in a way that could be used to design 2D metamaterials with multiple filtering capabilities

Geometry of the hierarchical perforated auxetic lattice

Wave propagation

Findings

Conclusion