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Mathematics and Mechanics of Solids
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Scattering of a Spherical Dyadic Field by a Small Rigid Sphere

George Dassios

Division of Applied Mathematics, Department of Chemical Engineering, University of Patras and ICEHT/FORTH, GR 26500 Patras, Greece

Katerina Karveli

Division of Applied Mathematics, Department of Chemical Engineering, University of Patras and ICEHT/FORTH, GR 26500 Patras, Greece

A complete dyadic field, which is generated at a point and propagates within a homogeneous and isotropic elastic medium, is disturbed by a small rigid sphere. Analytic solutions for this complicated dyadic scattering problem are provided with the help of an extended theory of the Papkovich representation for elastostatic dyadic fields. Relative results obtained numerically show an amazing coincidence as long as we stay in the low-frequency regime. In contrast to the plane wave excitation case, where only a few multipole terms are needed to express the leading low-frequency approximations, the case of point source excitation provides low-frequency solutions where an infinite number of multipoles are present. An exception is offered by the first-order approximation, which enjoys a closed-form expression.

Key Words: low-frequency scattering • scattering by a sphere • dyadic wave fields

Mathematics and Mechanics of Solids, Vol. 7, No. 1, 3-40 (2002)
DOI: 10.1177/1081286502007001219
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