EVALUATION OF THE ANISOTROPIC GREENS-FUNCTION IN 3-DIMENSIONAL ELASTICITY

A perturbation expansion technique for approximating the three dimensi onal anisotropic elastic Green's function is presented. The method emp loys the usual series for the matrix (I-A)(-1) to obtain an expansion in which the zeroth order term is an isotropic fundamental solution. T he higher order contributions are expressed as contour integrals of ma trix products, and can be directly evaluated with a symbolic manipulat ion program. A convergence condition is established for cubic crystals , and it is shown that convergence is enhanced by employing Voigt aver aged isotropic constants to define the expansion point. Example calcul ations demonstrate that, for moderately anisotropic materials, employi ng the first few terms in the series provides an accurate solution and a fast computational algorithm. However, for strongly anisotropic sol ids, this approach will most likely not be competitive with the Wilson -Cruse interpolation algorithm.