The Anti-plane Problem Of Uncircular Inclusion In A Infinite Piezoelectricity

In this paper, an un-circular piezoelectric inclusion embedded in an infinite piezoelectric matrix is analysed in the framework of linear piezoelectricity. Based on the conformal mapping theory, the fundamental solution is obtained for the case of a far-field anti-plane mechanical load and a far-field in-plane electrical load. Except that, stress and electric field concentrations at the boundary of matrix and inclusion are also studied. For the maximum electric and stress field depends on various material parameters, we select four cases to study the concentrations as follows: (1) Elastic dielectric inclusion in elastic dielectric matrix; (2) Piezoelectric inclusion in elastic matrix; (3) Elastic dielectric inclusion in piezoelectric matrix; (4) Piezoelectric inclusion in piezoelectric matrix. It is shown that both stress concentration and electric field concentration under mechanical load and electrical load are much higher than the highest of that under mechanical load or electrical load alone.