A new approach for electro-elastic analysis of piezoelectric fiber composites with arbitrary shaped inclusions under anti-plane shear and in-plane electric loadings

Electro-elastic analysis of piezoelectric fiber composites with arbitrary shaped inclusions subjected to far field uniform anti-plane shear and in-plane electric loadings is performed in this study in order to increase the electromechanical performance and protect the vulnerable piezoelectric inclusion from electromechanical damage. A three-phase model with a representative volume element of piezoelectric fiber composites with arbitrary shaped inclusions is proposed based on the generalized self-consistent theory. Meanwhile, a new conformal mapping method based on Cauchy integral and series expansion is also proposed to map an arbitrary two-connected domain into an annular domain. Both of the electro-elastic responses and the effective moduli of the piezoelectric fiber composites with arbitrary shaped inclusions for the anti-plane problem are obtained using the complex potentials in series form and the homogenization strategy. Comparisons with literature show a good agreement. Additionally, the effects of the fiber shape and the fiber volume fraction on the normal shear stress and the tangential electric field distributions outside the piezoelectric fiber, and the effective moduli are investigated using the proposed model and method. It is shown that the normal shear stresses and the tangential electric fields outside piezoelectric fiber have intense fluctuations at the corner of the inclusion. Both of the electro-elastic responses and the effective moduli of piezoelectric fiber composites become larger as the shape of piezoelectric inclusion sharpens and the fiber volume fraction increases. Furthermore, the proposed model and method can be used for determining the appropriate shape and volume fraction of the piezoelectric inclusion to significantly reduce stress and electric field concentrations around the inclusion and optimize the electromechanical performance of piezoelectric fiber composites.