Numerical approximations of Green.s functions for elastic anisotropic media by spherical harmonics, interaction energies of point defects

Fundamental solutions of elastostatics for infinite anisotropic media are obtained by numerical integration, and also by the finite element method for bounded sphere. These solutions are presented in the form of mean-squared approximation by the series of spherical harmonics Y_lm up to the order l = 10 (look for Online Support Data, pdf) as exemplified by the materials of different elastic symmetry: isotropic (concrete), cubic (Si), hexagonal (AlN), orthorhombic (MgSiO₃ in perovskite phase), tetragonal with 6 or 7 independent elastic constants (ZrSiO₄ and CaWO₄ respectively), trigonal with 6 or 7 constants (Al₂O₃ and dolomite), monoclinic (gypsum), triclinic (Al₂SiO₅). Using obtained Green's functions for each crystal, the energy of elastic interaction of a pair of point defects has been plotted as a function of angles of their mutual orientation.