Modeling of Three-Phase Fibrous Composite Using the Asymptotic Homogenization Method

Abstract

A three-phase concentric fiber-reinforced periodic composite is considered wherein the constituents exhibit piezoelectric properties. The cross-section of the periodic cell is a regular hexagon with two concentric circles and the periodicity is the same in two directions at an angle ~ /3. Simple closed-form expressions are obtained for the effective properties of this composite by means of the asymptotic homogenization method. Numerical computations have been done. The analytical solution of the required resulting plane- and antiplane-strain local problems, which turns out to be only two, makes use of potential methods of a complex variable and properties of Weierstrass elliptic and related functions of periods (1,0) and (cos ~ /3, sin ~ /3). Benveniste's universal type of relations for this composite are satisfied. Comparison with other models is shown.