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

Tom Shearer, William Parnell, I. David Abrahams

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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.
    Original languageEnglish
    Article number20150450
    JournalRoyal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
    Volume471
    Issue number2182
    DOIs
    Publication statusPublished - 8 Oct 2015

    Keywords

    • pre-stress
    • non-linear elasticity
    • scattering
    • inhomogeneous deformations
    • antiplane waves
    • elastomer

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