Scattering of long-wavelength elastic waves from localized defects in solids

It is shown that long-wavelength elastic scattering data from an arbitrary localized defect in a uniform isotropic medium has a maximum information content of 22 parameters which are characteristic of the defect. These parameters are shown to consist of the mass excess δM and the 21 independent components of a fourth-rank tensor Dijkl, that depends on the elastic moduli variation δcijkl and static response properties of the defect region. This tensor and the contracted forms Dij (=Dijkk/3) and D (=Dkk/3) allow partial ’’inversion’’ of scattering data to determine properties of the defect. In particular, it is shown how to estimate the orientation and maximum stress intensity factor for defects in the form of planar cracks, to obtain lower bounds to maximum defect dimensions, and to represent defects in the form of inclusions or voids as approximately equivalent ellipsoids. The results are pertinent to the quantification of nondestructive examination of materials for defects in their interiors.