Efficient finite element modelling of guided wave scattering from a defect in three dimensions

The scattering matrix (S-matrix) encodes the elastodynamic scattering behaviour of a defect. For the case of guided waves in the low-frequency regime, we explore how to minimise the number of incident/scattered directions used to accurately simulate the S-matrix of an arbitrary defect. The general approach is to use three-dimensional finite element (FE) analysis, implemented in a commercial FE package, to simulate the wave-defect interactions. The scattered wave field is measured at monitoring nodes on a circle that surrounds the defect. These scattered waves are decomposed into the multi-modal far-field scattering amplitudes. The angular order of the scattering is found and used to minimise the number of incident and scattered directions that must be computed. The method is then used to simulate the S-matrices of surface-breaking semi-elliptical cracks and circular through-holes with arbitrary sizes. It is found that the required number of incident/scattered directions varies with the scattered mode, and this is due to the differing scattering orders of these scattered fields. These results demonstrate how to achieve more efficient modelling of guided wave scattering, and also contribute to an understanding of experimental defect characterisation.