A geometrical theory of diffraction for crack-opening displacements (Q1111820)

We present a geometrical theory of diffraction which predicts the crack- opening displacements associated with the scattering of waves by a crack in a homogeneous, isotropic, linearly elastic medium. For the two- dimensional problem of scattering of plane waves by a crack of finite width, this theory agrees with the leading-order term in the asymptotic expansion of the exact solution. This theory fails at custics. For the problem of scattering of a normally incident plane wave with longitudinal motions by a penny-shaped crack, this theory when corrected for the presence of the caustic, agrees very well with numerical results.