Asymptotic Elastodynamic Green Function in the Kiss Singularity in Homogeneous Anisotropic Solids

The far-field asymptotic formula is derived for the elastodynamic Green function in the kiss singularity in homogeneous anisotropic solids. In contrast to standard asymptotics in regular directions the derived formula is more complex and expressed in the form of a 1-D integral. This integral is specified for the kiss singularity along the symmetry axis in transverse isotropy and along the fourfold symmetry axes in tetragonal and cubic symmetries. The shape of the slowness surface in the singularity is regular in transverse isotropy and the amplitude of the Green function is expressed by means of the Gaussian curvature of this surface in the singularity. However, the shape of the slowness surface is irregular and the Gaussian curvature is not defined in the singularity in tetragonal or cubic symmetries. In this case, the amplitude of the Green function is expressed by means of the generalized Gaussian curvature.