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

Published online by Cambridge University Press:  20 August 2015

William J. Parnell  and
I. David Abrahams
William J. Parnell*
Affiliation:
School of Mathematics, Alan Turing Building, University of Manchester, Manchester, M13 9PL, UK
I. David Abrahams*
Affiliation:
School of Mathematics, Alan Turing Building, University of Manchester, Manchester, M13 9PL, UK
*
Corresponding author.Email:william.parnell@manchester.ac.uk
Email address:david.abrahams@manchester.ac.uk
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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 r0 (R0) 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 r0, but instead on the original void size A and original distance R0.

Keywords

74B1574B2074J2074Q15Pre-stressincompressibleneo-Hookeanrubberincremental SH wavesscatteringline source
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 367 - 382
Copyright
Copyright © Global Science Press Limited 2012

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