Interface energy effect on electromechanical response of piezoelectric composites with an arbitrary nano-inclusion under anti-plane shear

For piezoelectric composites with nano-inclusions, the interface energy around the nano-inclusions will play important roles in predicting the electromechanical response under different loadings. In this paper, the interface energy effect on the electromechanical response of piezoelectric composites with a coated nano-inclusion of arbitrary shape under anti-plane mechanical and in-plane electric loadings is studied, and the analytical solutions of the stress and electric displacement are presented. Combining the Laurent series expansion technique and conformal mapping method, the general solutions of complex potentials are expressed. The unknown coefficients are determined by satisfying the boundary conditions with consideration of surface/interface effect. Some examples such as triangle and quasi-square shapes of nano-inclusions are given to show the distribution of internal stress and electric field. It is found that the interface energy effect shows significant variation with the shapes of nano-inclusions, and the effect in the case of circular shape is the smallest. The interface effect on the stress and electric field at the inner and outer boundaries is also examined.