An inverse scattering method to characterize inhomogeneities in elastic solids

An inverse method for ultrasonic scattering data is proposed to characterize a single elastic inhomogeneity of general shape contained in an elastic solid. The method is based on an integral representation for the scattered field in the frequency domain. The method has been applied at both large and intermediate wavelengths as compared with a characteristic length parameter of the scatterer. For a given scattered field the inverse problem has been formulated as a nonlinear optimization problem. At low frequencies its solution gives the location of the centroid of the scatterer, the equivalent force vector, and the moment tensor. In addition, the interaction energy between the material and the inclusion is obtained for a related static stress state. This latter result may have relevance to failure conditions in the material under service conditions. For intermediate frequencies, the volume and elastic constants of an equivalent spherical inhomogeneity are obtained, in addition to its position.