Scattering by two penny-shaped cracks with spring boundary conditions

The elastodynamic scattering by a penny-shaped crack with spring boundary conditions is investigated. The transition (T) matrix of the crack is determined and the usefulness of this is illustrated by considering also the scattering by two cracks. The T matrix of a single crack is first determined by a direct integral equation method which gives the crack-opening displacement and the integral representation which subsequently gives the scattered field expanded in spherical waves. Two cracks are considered by a multi-centred T matrix approach where matrix inverses are expanded in Neumann series. Rotation matrices are employed so that the cracks may have an arbitrary orientation. 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.