Antiplane elastic wave cloaking using metamaterials,homogenization and hyperelasticity |
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Authors: | William J Parnell Tom Shearer |
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Institution: | School of Mathematics, Alan Turing Building, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom |
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Abstract: | We consider the problem of how to cloak objects from antiplane elastic waves using two alternative techniques. The first is the use of a layered metamaterial in the spirit of the work of Torrent and Sanchez-Dehesa (2008) who considered acoustic cloaks, motivated by homogenization theories, whilst the second is the use of a hyperelastic cloak in the spirit of the work of Parnell et al. (2012). We extend the hyperelastic cloaking theory to the case of a Mooney–Rivlin material since this is often considered to be a more realistic constitutive model of rubber-like media than the neo-Hookean case studied by Parnell et al. (2012), certainly at the deformations required to produce a significant cloaking effect. Although not perfect, the Mooney–Rivlin material appears to be a reasonable hyperelastic cloak. This is clearly encouraging for applications. We quantify the effectiveness of the various cloaks considered by plotting the scattering cross section as a function of frequency, noting that this would be zero for a perfect cloak. |
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Keywords: | Antiplane waves Cloaking Metamaterials Hyperelasticity Homogenization |
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