Calculation of the Electroelastic Green's Function of the Hexagonal Infinite Medium

TL;DR

This paper derives an explicit closed-form electroelastic Green's function for an infinite hexagonal piezoelectric medium, enabling advanced analysis of electroelastic fields in such materials.

Contribution

The paper provides the first explicit closed-form calculation of the electroelastic Green's function for a hexagonal piezoelectric medium, extending previous elastic and electric solutions.

Findings

Green's function matches known elastic and electric solutions in special cases

Explicit formulas facilitate calculation of the electroelastic Eshelby tensor

Residue calculation method effectively derives the Green's function

Abstract

The electroelastic 4 $\times$ 4 Green's function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly 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: Kr{\"o}ner '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].