Some asymptotic expansions of components of Eshelby tensor in cases of cubic and hexagonal anisotropy

A method is suggested for calculating Eshelby tensor for anisotropic media with the help of asymptotic expansion over a small parameter corresponding to deviation of elasticity tensor from a case for which Eshelby tensor may be expressed in terms of elementary function. Cases of cubic and hexagonal anisotropy are considered. For cubic crystals the solution is obtained as a series of correcting terms to be added to the solution for isotropic media. In case of hexagonal crystals at first stage a solution in terms of elementary functions are found for the particular type of hexagonal crystal (where only three of five elastic constant are independent), at the second stage the solution for the hexagonal crystal of general type is found as a series of correcting terms to be added to the solution for the hexagonal crystal of the particular type. Spherical, penny-shaped and needle-like inclusions are considered in case of cubic anisotropy, penny-shaped and needle-like inclusions are considered in case of hexagonal anisotropy. The applicability ranges of the obtained solutions were estimated.