Elastic Wave Scattering Calculations and the Matrix Variational Padé Approximant Method

The matrix variational Padé approximant and its generalization to elastic wave scattering are discussed. Predictions of the method for the scattering of a longitudinal plane wave are compared with the exact scattering from spherical voids and inclusions. Its predictions are also compared to those of the first and second Born approximations and to the standard matrix Padé approximant based on these Born approximations

Long Wave Scattering of Elastic Waves from Volumetric and Crack-Like Defects of Simple Shapes

The development of several approximations appears to permit accurate and practical calculations of the scattering of elastic waves from volumetric and crack-like defects of simple shapes if the wavelength of the incident wave is larger than the characteristic length of the shape. These approximations, which I call the quasi-static and extended quasi-static, use static solutions of defects in uniform strains to predict scattered (dynamic) fields. Since static solutions for several simple defect shapes (oblate and prolate spheroid, ellipsoid, and circular and elliptical cracks) are available, scattering predictions are possible, and the results of such calculations are presented