# Elastic Wave Scattering by Closed Cracks and Thin Flaws - Multiple Scattering and Resonances

Sammanfattning: In this thesis we study elastic wave scattering by thin flaws and closed cracks, which finds applications in ultrasonic testing and evaluation of materials.

First we consider the scattering of an SH-wave by a thin finite elastic layer between two elastic half-spaces. The layer, thin compared to the wavelengths involved, is modelled by spring boundary conditions extended with terms accounting for inertia forces. A direct integral equation method is used, with the discontinuity of displacement and traction over the thin layer as the unknowns. Numerical results are given for the scattered energy and the far field amplitude.

We also investigate the elastodynamic scattering by two penny-shaped cracks with spring boundary conditions in the fully three-dimensional case. The transition matrix of a single crack is first determined by a direct integral equation method which gives the crack-opening displacement (COD) and the integral representation which subsequently gives the scattered field expanded in spherical waves. Two cracks are considered by a multi-centered T matrix approach where the matrix inverses are expanded in Neumann series. Rotation matrices are employed so that the cracks may have an arbitrary orientation. The numerical procedures are very stable and it has been possible to go to quite high frequencies. The back-scattered longitudinal far field amplitude is computed both in the frequency and time domain in a few cases and the effects due to multiple scattering are in particular explored.

The natural frequencies of one partially closed penny-shaped crack are calculated for the symmetric part of the problem. The natural frequencies are given as the complex SEM (singularity expansion method) poles of the symmetric part of the T matrix. A clear correlation is shown between the migration of the poles, as the crack gets more closed, and the frequencies at which the scattering cross section has its peaks.

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