The Effective Properties of One-Dimensional Orthorhombic Piezoelectric Quasicrystal Materials Containing Ellipsoidal Inclusions

Eshelby tensors serve as the basis of micromechanics which should be explored first to study the effective mechanical behavior of heterogeneous materials. In this paper, the Eshelby tensor is generalized from isotropic materials to quasicrystals. By utilizing Green's functions and Cauchy's residue theorem, simple and unified expressions of Eshelby tensors for one-dimensional (1D) orthorhombic piezoelectric quasicrystal are derived. Specifically, the closed-form Eshelby tensors are given when the shape of the inclusions is elliptic cylinder. Furthermore, the effective stiffnesses of 1D orthorhombic piezoelectric quasicrystal are obtained in view of the received Eshelby tensors and the Mori-Tanaka mean theory. Finally, parameter studies are carried out, and the effect of material properties and volume fraction on the effective overall material properties are investigated.