The precise evaluation of derivatives of the anisotropic elastic Green's functions

Using Fourier transforms a simple scheme for numerically obtaining derivatives of the tensor Green's functions of elasticity with great precision is derived. The technique developed circumvents the need for solving an auxiliary eigenvalue problem and a related sextic algebraic equation common to previous treatments of this problem. Numerical results for the dilatation associated with a “dilatation center” in copper are given. The speed and accuracy of the present technique indicates that a previous suggestion by Lothe is indeed quite practical — namely, that internal stress problems (dislocations, point defects, inclusions, thermal stresses) in anisotropic media may be treated using tabulated data for the Green's functions and their derivatives.