Application of Mori-Tanaka method in 3-1 porous piezoelectric medium of crystal class 6

We consider a piezoelectric medium of hexagonal crystal system of class 6 containing a uniform distribution of circular cylindrical inclusions aligned with the axis of material symmetry. We determine the piezoelectric Eshelby tensor explicitly. In the case of cylindrical holes, we use the Eshelby tensor together with the multiscale Mori-Tanaka Method to obtain analytical formulae for the effective electroelastic properties of the homogenized medium. These formulae depend upon both the electroelastic properties of the matrix material and the volume fraction of the cylindrical holes. Using electroelastic properties reported in the literature, we obtain graphs of the effective properties of the porous medium versus the volume fraction of the pores and show that these effective electroelastic properties decrease for increasing porous volume fraction, as expected. In particular, for the case of the crystal subclass 6 mm, the results obtained via Mori-Tanaka Method agree well with results obtained via Method of Asymptotic Homogenization and Finite Element Method. This work is important in the evaluation of the effective electroelastic properties of heterogeneous solids with hierarchical structures, such as bones.