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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 Ylm 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.
Keywords: elastic anisotropic media; Green.s functions; spherical harmonics; numerical approximations; point defects. |
full paper (pdf, 2192 Kb)
Online Support Data (pdf, 976 Kb)