Volume 11, Issue 2
Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material

William J. Parnell & I. David Abrahams

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

Published online: 2012-12

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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.

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@Article{CiCP-11-367, author = {}, title = {Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {367--382}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.111209.160610s}, url = {http://global-sci.org/intro/article_detail/cicp/7367.html} }
TY - JOUR T1 - Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material JO - Communications in Computational Physics VL - 2 SP - 367 EP - 382 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.111209.160610s UR - https://global-sci.org/intro/article_detail/cicp/7367.html KW - AB -

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.

William J. Parnell & I. David Abrahams. (2020). Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material. Communications in Computational Physics. 11 (2). 367-382. doi:10.4208/cicp.111209.160610s
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