Derivatives of Green’s functions in piezoelectric media and their application in dislocation dynamics

Three-dimensional extended Green’s functions and their high-order derivatives in general anisotropic piezoelectric materials are derived and expressed in integral forms. They can be evaluated directly by the Gaussian numerical integration method. The extended Green’s functions and their derivatives by the present method have accuracy and computational efficiency. Using the extended Green’s functions, the stress field induced by an arbitrary dislocation in an anisotropic piezoelectric medium, is obtained and expressed as a line integral around the dislocation.