On the effective electroelastic properties of piezoelectric composites containing spatially oriented inclusions

Presented here is an analytical method for determining the effective electroelastic properties of piezoelectric composites containing spatially oriented inclusions. Both inclusion and matrix are assumed to be linearly piezoelastic. The three-dimensional anisotropic inclusion method has been developed, and the explicit expressions for the electrostatic tensors analogous to the Eshelby tensors for elastic ellipsoidal inclusions have been obtained. With these tensors, analytical expressions for the electroelastic fields of the piezoelectric composite can be established. Based upon the Mori-Tanaka mean field theory to account for the interaction between the inclusions and matrix, the effective electroelastic properties (elastic, piezoelectric and dielectric constants) of the composites are expressed analytically in terms of phase properties, orientation angles, volume fraction and shape. Numerical results have been given for a BaTiO,/PZT-5H composite. The results indicate that the proposed methods yield identical results whether a traction-electric displacement or an elastic displacement-electric field is prescribed on the composite boundary is self-consistency. The electromechanical coupling due to the piezoelastic effect is found to be strongly affected by both the volume fraction and the orientation of inclusions. 0 1997 Elsevier Science Ltd