Piezoelectric Study on Elliptic Inhomogeneity Problem Using Alternating Technique

This paper presents a novel efficient procedure to analyze the elliptical inhomogeneity problem in piezoelectric materials under electromechanical loadings. The electromechanical loadings considered in this paper include a point force and a point charge or a far-field anti-plane shear and in-plane electric field. The analytical continuation method together with alternating technique is used to derive the electroelastic fields in terms of the corresponding homogeneous solution. Compared to existing related papers, this approach could lead to some interesting simplifications in solution procedure and the derived analytical solution for singularity problems can be employed as a Green's function to investigate matrix cracking in the inclusion/matrix system. Numerical results are provided to show the effect of the material mismatch, the aspect ratio and the loading condition on the electroelastic field due to the presence of the inhomogeneity.