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Numerical modelling of ultrasonic scattering by cracks

: Langenberg, K.-J.; Schmitz, V.

Proceedings of the 3rd German-Japanese Joint Seminar
Deutsch-Japanisches-Seminar <3, 1985, Stuttgart>
Fraunhofer IZFP ()
Beugung; Elastodynamik; Modellierung; Physikalische Optik; Riß

Two basic aspects of numerical modelling of ultrasonic wave scattering by cracks in solids are discussed in the present paper: how do several standard mathematical procedures to obtain numerical values for scattered fields compare with respect to validity and accuracy, and what conclusions can be drawn from the spatial and temporal structure of these fields for identification and imaging purposes. For simplicity, the model of a plane twodimensional strip-like scatterer with stress-free boundary condition embedded in linear, homogeneous and isotropic solid has been chosen, and scattering amplitudes for P-P, P-SV, SV-SV, SV-P wave fields are compared with respect to the methods of eigenfunction expansions (EIFU), numerical solution of integral equations (INT), elastodynamic physical optics (EPO) and elastodynamic geometric theory of diffraction (GTD). The first two methods are supposed to yield "exact" numerical results, whereas EPO and GTD rely on physical assumptions to yield simplifie d approximate but analytical expressions whose range of validity could then be investigated by comparison with the "exact" results giving rise to an estimation of their applicability. The integral equation method is then utilized to yield scattered fields in the time domain for pulsed excitation. Comparison with easily interpretative GTD-results exhibits specific features of these transients in terms of wavefronts and resonances, which form the basis of appropriate imaging and identification algorithms.