Reflection of elastic waves by a distribution of coplanar cracks

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Abstract
A method is presented to evaluate quantitatively the reflection of elastic waves by a distribution of coplanar cracks. The method is based on a novel calculation of crack-opening volumes. To compute the crack-opening volume of a specified crack, the effects of neighboring cracks are approximated by the effects of pairs of vector dipoles at the geometrical centers of those cracks. The strengths of the dipoles are proportional to the crack-opening volumes of the neighboring cracks. Thus a crack-opening volume is expressed as a superposition of solutions of two generic problems. One concerns the interaction of the incident wave with a single crack, while the other is concerned with the interaction of a vector dipole with a single crack. For a plane containing a large number of cracks, closed-form expressions have been derived for the reflection and transmission coefficients in terms of the crack-opening volumes. The results have been generalized to statistical distributions of cracks.

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