Commun. Comput. Phys., 11 (2012), pp. 367-382.


Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material

William J. Parnell 1*, I. David Abrahams 1

1 School of Mathematics, Alan Turing Building, University of Manchester, Manchester, M13 9PL, UK.

Received 11 December 2009; Accepted (in revised version) 16 June 2010
Available online 24 October 2011
doi:10.4208/cicp.111209.160610s

Abstract

An isolated cylindrical void is located inside an incompressible nonlinear-elastic medium whose constitutive behaviour is governed by a neo-Hookean strain energy function. In-plane hydrostatic pressure is applied in the far-field so that the void changes its radius and an inhomogeneous region of deformation arises in the vicinity of the void. We consider scattering from the void in the deformed configuration due to an incident field (of small amplitude) generated by a horizontally polarized shear (SH) line source, a distance r_0 (R_0) away from the centre of the void in the deformed (undeformed) configuration. We show that the scattering coefficients of this scattered field are unaffected by the pre-stress (initial deformation). In particular, they depend not on the deformed void radius a or distance r_0, but instead on the original void size A and original distance R_0.

AMS subject classifications: 74B15, 74B20, 74J20, 74Q15

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Key words: Pre-stress, incompressible, neo-Hookean, rubber, incremental SH waves, scattering, line source.

*Corresponding author.
Email: william.parnell@manchester.ac.uk (W. J. Parnell), david.abrahams@manchester.ac.uk (I. D. Abrahams)
 

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