Nonlinear pre-stress for cloaking from antiplane elastic waves

Parnell, William J. (2012) Nonlinear pre-stress for cloaking from antiplane elastic waves. Proceedings of the Royal Society, 468 (2138). pp. 563-580.

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Abstract

A theory is presented showing that cloaking of objects from antiplane elastic waves can be achieved by elastic pre-stress of a neo-Hookean nonlinear elastic material. This approach would appear to eliminate the requirement of metamaterials with inhomogeneous anisotropic shear moduli and density. Waves in the pre-stressed medium are bent around the cloaked region by inducing inhomogeneous stress fields via pre-stress. The equation governing antiplane waves in the pre-stressed medium is equivalent to the antiplane equation in an unstressed medium with inhomogeneous and anisotropic shear modulus and isotropic scalar mass density. Note however that these properties are induced naturally by the pre-stress. Since the magnitude of pre-stress can be altered at will, this enables objects of varying size and shape to be cloaked by placing them inside the fluid-filled deformed cavity region.

Item Type:	Article
Uncontrolled Keywords:	Cloaking, antiplane waves, pre-stress, neo-Hookean
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
Depositing User:	Dr William J Parnell
Date Deposited:	06 Mar 2012
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1787

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