Antiplane wave scattering from a cylindrical cavity in pre-stressed non-linear elastic media

Shearer, Tom and Parnell, William J. and Abrahams, I. David (2015) Antiplane wave scattering from a cylindrical cavity in pre-stressed non-linear elastic media. Proceedings of the Royal Society A. ISSN 1471-2946

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Abstract

The effect of a longitudinal stretch and a pressure-induced inhomogeneous radial deformation on the scattering of antiplane elastic waves from a cylindrical cavity is determined. Three popular non-linear strain energy functions are considered: the neo-Hookean, the Mooney-Rivlin and a two-term Arruda-Boyce model. A new method is developed to analyse and solve the governing wave equations. It exploits their properties to determine an asymptotic solution in the far-field, which is then used to derive a boundary condition to numerically evaluate the equations local to the cavity. This method could be applied to any linear ordinary differential equation whose inhomogeneous coefficients tend to a constant as its independent variable tends to infinity. The effect of the pre-stress is evaluated by considering the scattering cross-section. A longitudinal stretch is found to decrease the scattered power emanating from the cavity, whereas a compression increases it. The effect of the pressure difference depends on the strain energy function employed. For a Mooney-Rivlin material, a cavity inflation increases the scattered power and a deflation decreases it; for a neo-Hookean material, the scattering cross-section is unaffected by the radial deformation; and for a two-term Arruda-Boyce material, both inflation and deflation are found to decrease the scattered power.

Item Type: Article
Uncontrolled Keywords: pre-stress, non-linear elasticity, scattering, inhomogeneous deformations, antiplane waves, elastomer
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
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 80 INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY > 89 Other areas of applied and interdisciplinary physics
Depositing User: Dr Tom Shearer
Date Deposited: 02 Oct 2015
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2392

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