Antiplane elastic wave cloaking using metamaterials, homogenization and hyperelasticity

Parnell, William J. and Shearer, Tom (2013) Antiplane elastic wave cloaking using metamaterials, homogenization and hyperelasticity. Wave Motion, 50. pp. 1140-1152. ISSN 0165-2125

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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.

Item Type: Article
Uncontrolled Keywords: Antiplane waves Cloaking Metamaterials Hyperelasticity Homogenization
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 46 Continuum mechanics of solids
Depositing User: Dr Tom Shearer
Date Deposited: 08 Dec 2014
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2202

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