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Bonnet, Marc

Solvability of a volume integral equation formulation for anisotropic elastodynamic scattering. (English) Zbl 1383.35226

J. Integral Equations Appl. 28, No. 2, 169-203 (2016).
Summary: This article investigates the solvability of volume integral equations arising in elastodynamic scattering by penetrable obstacles. The elasticity tensor and mass density are allowed to be smoothly heterogeneous inside the obstacle and may be discontinuous across the background-obstacle interface, the background elastic material being homogeneous. Both materials may be anisotropic, within certain limitations for the background medium. The volume integral equation associated with this problem is first derived, relying on known properties of the background fundamental tensor. To avoid difficulties associated with existing radiation conditions for anisotropic elastic media, we also propose a definition of the radiating character of transmission solutions. The unique solvability of the volume integral equation (and of the scattering problem) is established. For the important special case of isotropic background properties, our definition of a radiating solution is found to be equivalent to the Sommerfeld-Kupradze radiation conditions. Moreover, solvability for anisotropic elastostatics, directly related to known results on the equivalent inclusion method, is recovered as a by-product.

Cited in 2 Documents

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
35P25 Scattering theory for PDEs
35J15 Second-order elliptic equations
45F15 Systems of singular linear integral equations
74J20 Wave scattering in solid mechanics

Keywords:

volume integral equation; elastodynamics; anisotropy; scattering
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Full Text: DOI Euclid

References:

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