ELASTIC GREENS FUNCTION FOR ANISOTROPIC CUBIC CRYSTALS

The Green's function describing the elastic displacement due to a unit force in an infinite cubic material is investigated in detail. Only for special cases can an exact solution be given, i.e., for c11-c12-2c44=0 (isotropy), for c12+c44=0, and for <100> directions. Perturbation theory is applied to the cases where these conditions are only approximately fulfilled. Divergencies or strong maxima of the Greens' function, occurring in nearly unstable materials for c11-c120 or c440, are examined. Analytical approximations for the Green's function are given by fitting the exact known Fourier transform with a suitably chosen ansatz in certain directions. Other simple approximations are derived by variational techniques and give good results for crystals with small and medium anisotropy. © 1969 The American Physical Society.