Elastic wave propagation in general transversely isotropic media. I. Green’s functions and elastodynamic holography

Abstract

The formalism of plane-wave spectral decomposition of elastic wave fields is used to derive a simple method for solving the inverse scattering problem, which can also be regarded as a basis for further imaging techniques. For transversely isotropic materials like fiber composites, but also, e.g., unidirectionally grain-structured austenitic steels, the elastodynamic dyadic and triadic Green’s functions are derived in form of their two-dimensional space-time spectral representations. Based on a theory of plane-wave propagation in these media [], the resulting expressions appear in a coordinate-free form and contain the orientation of the materials’ fiber axis as an additional parameter. Thus the results are particularly useful for extension to the case of layered material. The formulation of Huygens’ principle for a source-free half-space provides the socalled elastodynamic holography, which allows forward-backward propagation of elastic wave fields in form of an integral representation for the displacement vector. This representation is evaluated with respect to space and time via fast Fourier transforms, the effectiveness of the resulting imaging algorithm is demonstrated in comparison with the conventional isotropic algorithm used so far. The integral representation mentioned above is derived for given displacement in a reference plane (specimen surface), the derivation for the case of given surface traction will follow in the second part of this presentation, providing an integral representation for the transducer field.