Polarization approach to the scattering of elastic waves—I. Scattering by a single inclusion

doi:10.1016/0022-5096(80)90021-6

Journal of the Mechanics and Physics of Solids

Volume 28, Issues 5–6, December 1980, Pages 287-305

https://doi.org/10.1016/0022-5096(80)90021-6 Get rights and content

Abstract

Scattering problems in elastodynamics are formulated in terms of integral equations, whose kernels are obtained from the Green's function for a comparison body. The comparison body will usually be taken as homogeneous and elastic in applications but, at least formally, there is no bar to its being inhomogeneous, viscoelastic and non-local. The novel feature of the formulation is the introduction of a “momentum polarization” to cope with density variations in a way that exactly parallels the stress polarization's correspondence with variations in moduli. To illustrate the use of the equations, scattering by an ellipsoidal inhomogeneity in a generally anisotropic matrix is studied in the Rayleigh limit and an asymptotic formula for its scattering cross-section is given. Detailed results are presented for a spheroidal inhomogeneity in an isotropic matrix, with explicit limiting forms for the scattering cross-sections of penny-shaped cracks, rigid circular discs and rigid needles.

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Polarization approach to the scattering of elastic waves—I. Scattering by a single inclusion

Abstract

Q. appl. Math.

Q. appl. Math.

J. acoust. Soc. Am.

SIAM J. appl. Math.

Z. Phys.

J. appl. Phys.

J. Elast.

Generalized Functions

J. appl. Phys.

J. appl. Phys.

J. appl. Phys.

J. appl. Phys.

J. appl. Phys.

J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids