Eshelby tensors and effective stiffness of one-dimensional orthorhombic quasicrystal composite materials containing ellipsoidal particles.

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, Eshelby tensors are extended 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 quasicrystal are derived. Specifically, the closed-form Eshelby tensors are given when the shapes of the inclusions are spheroid, elliptic cylinder, rod-shaped, penny-shaped, and ribbon-like, respectively. Furthermore, the effective stiffnesses of 1D orthorhombic 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. [ABSTRACT FROM AUTHOR]