Two-Dimensional Piezoelectric Quasicrystal Eshelby Tensors for an Elliptical Inclusion

Eshelby tensors is the basis of the micromechanics theory of composite materials and it is the key to solve the inclusion problem. In this paper, the Eshelby tensors of elastic isotropic inclusions are extended to the case of two-dimensional piezoelectric quasicrystal. By employing the Cauchy’s residue theorem, simplified and closed-form expressions of the two-dimensional piezoelectric quasicrystals Eshelby tensors of an elliptical inclusion embedded in the piezoelectric matrix are obtained. In the present theory, the coupling effect of phonon field, phason field and electric field are considered. These solutions are verified by degrading the quasicrystals into isotropic materials. Finally, some numerical results are investigated to shown the effect of the aspect ratio on the Eshelby tensors, which shown out the electric field affect the Eshebly tensors obviously. The obtained solutions can serve as the theoretical basis for the potential application in the field as fracture mechanics, piezoelectric composites, thermal and defection-related composites.