Mean-field T-matrix approach to elastic wave scattering by small and point-like objects

The T-matrix of a small inclusion embedded in a homogeneous matrix is calculated for vector elastic waves. The theory relies on an approximation of the local stress and momentum inside the inclusion by volumetric averages, which allows the summation of the full multiple-scattering series. The limiting case of a point scatterer is discussed. The mean-field T-matrix and its point limit both satisfy the elastodynamic version of the optical theorem. The accuracy of the results is discussed by comparison with some exact solutions for spheres. In particular, the mean-field T-matrix allows the approximate modeling of low-frequency resonances by small, high-contrast objects. The present theory could be applied to the multiple scattering of elastic waves by a collection of small or fuzzy resonant scatterers.