  In this work, dislocation master-equations valid for anisotropic materials
are derived in terms of kernel functions using the framework of micromechanics.
The second derivative of the anisotropic Green tensor is calculated in the
sense of generalized functions and decomposed into a sum of a $1/R^3$-term plus
a Dirac $\delta$-term. The first term is the so-called "Barnett-term" and the
latter is important for the definition of the Green tensor as fundamental
solution of the Navier equation. In addition, all dislocation master-equations
are specified for Somigliana dislocations with application to 3D crack
modeling. Also the interior Eshelby tensor for a spherical inclusion in an
anisotropic material is derived as line integral over the unit circle.
