title: Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media.
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 nonlinear 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.
authors.affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.
authors.forename: Tom
authors.initials: T
authors.lastname: Shearer
authors.affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.
authors.forename: William J
authors.initials: WJ
authors.lastname: Parnell
authors.affiliation: School of Mathematics , University of Manchester , Oxford Road, Manchester M13 9PL, UK.
authors.forename: I David
authors.initials: ID
authors.lastname: Abrahams
keywords: antiplane waves; elastomer; inhomogeneous deformations; nonlinear elasticity; pre-stress; scattering