Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials

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• 作者：Ké ; vin Billon^a ; Ioannis Zampetakis^b ; ^d ; Fabrizio Scarpa^b ; Morvan Ouisse^a ; ^{morvan.ouisse@femto-st.fr} ; Emeline Sadoulet-Reboul^a ; Manuel Collet^c ; Adam Perriman^d ; Alistair Hetherington^e
• 关键词：Periodic structures ; Metamaterial ; Auxetic ; Vibroacoustic
• 刊名：Composite Structures
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：160
• 期：Complete
• 页码：1042-1050
• 全文大小：1834 K
• 卷排序：160

文摘

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.