Dyadic scattering by small obstacles. The rigid sphere

The general theory of low-frequency dyadic scattering is developed for the near fields, the far fields and all the energy functionals associated with scattering problems. The incident field could be any complete dyadic field generated either in the exterior medium of propagation (point source) or at infinity (plane waves). The case of a small rigid sphere, which is illumin ated by a plane dyadic field, is solved and the corresponding results for a coustic and elastic scattering are recovered as special cases. In order to solve analytically the sphere problem a special technique had to be develop ed, which generates Papkovich-type differential representations of dyadic e lastostatic displacements. Comparison of numerical results, obtained via th e boundary element method, show an amazing accuracy with our analytical res ults.