### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 2pSA4. Calculation of diffraction coefficients for a crack in an
anisotropic solid.

**Gerry R. Wickham
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*Dept. of Mathematics and Statistics, Brunel Univ., Uxbridge, Middlesex UB8
3PH, UK
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**Patricia A. Lewis
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*Bolton Inst., Bolton BL3, UK
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The diffraction of sound by a semi-infinite planar crack arbitrarily
oriented in a homogeneous anisotropic linearly elastic solid is considered. The
problem is formulated exactly as an integrodifferential equation with a
difference kernel which is the stress tensor corresponding to the fundamental
point force solution for the uncracked solid. The solution of this equation is
the crack opening displacement (COD) induced by the incident field and this may
be expressed in terms of the Wiener--Hopf factors of the Fourier symbol of the
kernel. The quantity of physical interest is the diffraction coefficient which
is proportional to the Fourier transform of the COD and relates the vector
amplitude on an incident ray to the crack edge, to the amplitudes on the
diffracted rays. In the general case, the necessary Wiener--Hopf factorization
cannot be found explicitly. However, by exploiting the fact that the diffraction
coefficient is independent of frequency, it is possible to develop a novel
numerical scheme for its evaluation. The exact diffracted field is then
analytically expressed in terms of these coefficients. It is shown how the rich
qualitative geometrical structure of the diffracted field may be obtained and
how the solution reproduces known results for special material symmetries.