Computing forces on interface elements exerted by dislocations in an   elastically anisotropic crystalline material
  Driven by the growing interest in numerical simulations of dislocation-interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple dislocation dynamics with a finite element or boundary element solver. The dislocation stress fields in elastically anisotropic media are made analytically accessible through the spherical harmonics expansion of the derivative of Green's function, and analytical expressions for the forces on interface elements are derived by analytically integrating the spherical harmonics series recursively. Compared with numerical integration by Gaussian quadrature, the newly developed analytical algorithm for interface traction integration is highly beneficial in terms of both computation precision and speed. 
Bing Liu, Athanasios Arsenlis, Sylvie Aubry
cond-mat.mtrl-sci