Time-domain elastodynamic scattering problems

Abstract

The interaction of an ultrasonic pulse with an inhomogeneity in an elastic solid is generally analyzed by the use of the FFT over time in combination with a numerical method for the scattering problem in the frequency domain. For pulses with a high-frequency content this approach tends to be computationally intensive. In this talk the possibilities of a direct analytical time-domain approach are explored, and then there is a discussion of numerical techniques. Results are presented for a single crack (slit and penny-shaped) and for macrocrack-microcrack configurations. Some of these results have been obtained by the finite difference method. The main emphasis in this paper is, however, on the development of a time-domain boundary integral equation method. By the use of appropriate representation integrals, a system of boundary integral equations has been obtained, which has subsequently been cast in a form that is amenable to a solution by the boundary element method in conjunction with a time-stepping technique. Particular attention has been devoted to dynamic overshoots of the stress intensity factors. Elastodynamic stress intensity factors have been computed as functions of time, and they have been compared with results of other authors.