Relationship between contact and crack problems for generally anisotropic bodies

The author has noticed in two previously published articles that the kernels of the governing integral equations for normal contact and crack problems in the case of transversely isotropic bodies had an interesting property, namely, the integrands of their Fourier transform representations were inverse to one another. Presuming that this property was not accidental, the author decided to check whether this property would hold in the case of general anisotropy. The result was positive and hence this article. It does not look like this property was previously noticed by other authors. It is also shown that the kernel of the governing integral equations can be computed exactly and in closed form, using the theory of generalized functions. We point out though that close form kernel contains the roots of the sixth order algebraic equation, for which no closed form solution exists.