Calculation of the electroelastic Green’s function of the hexagonal infinite medium

Abstract

The electroelastic 4 × 4 Green's function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitely in closed compact form (eqs. (73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm's method [2]. In the case of vanishing piezoelectric coupling the derived Green's function coincides with two well known results: Kröner's expressions for the elastic Green's function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge.The obtained electroelastic Green's function is useful for the calculation of the electroelastic Eshelby tensor [16].

Dynamic potentials and Green's functions of a quasi–plane piezoelectric medium with inclusion

“…For the piezoelectric 3D infinite medium of transversely isotropic symmetry, formulations of the static Green function were given by Deeg (1980) and Chen (1993), among others. In compact closed form this Green function was derived by Michelitsch (1997) in a form convenient for applications to inclusion and inhomogeneity problems (e.g. Levin et al .…”