Inclusions and inhomogeneities in electroelastic media with hexagonal symmetry

Abstract:

For a long time, the absence of explicit Green's functions (fundamental solutions) for electroelastic media has hindered progress in the modelling of the properties of piezoelectric materials. Michelitsch's recently derived explicit electroelastic Green's function for the infinite medium with hexagonal symmetry (transversely isotropic medium) [4] is used here to obtain compact closed-form expressions for the electroelastic analogue of the Eshelby tensor for spheroidal inclusions. This represents a key quantity for the material properties of piezoelectric solids and analysis of the related electroelastic fields in inclusions. For the limiting case of continuous fibers our results coincide with Levin's expressions [8]. The derived method is useful for an extension to non-spheroidal inclusions or inhomogeneities having an axis of rotational symmetry parallel to the hexagonal c-axis.