Anti-plane Greenʹs functions and cracks for piezoelectric material with couple stress and electric field gradient effects

This research is concerned with the anti-plane strain problems of polarized ceramics with both the couple stress and electric field gradient effects. This theory possesses two characteristic lengths l 1 and l 2 which are determined explicitly. In addition the two characteristic lengths can be either positive real or complex conjugate with positive real part. We first investigate the electroelastic field induced by a static line force and a line charge. It is found that the displacement and the electric potential are regular at the point where the line force and line charge are located. We then consider the near-tip asymptotic electroelastic field for a mode III crack. The analysis demonstrates that the near-tip asymptotic electroelastic field is governed by two parameters B and D. The total stresses and in-plane electric displacements exhibit the stronger r − 3 / 2 singularity near the crack tip; while the couple stresses, the out-of-plane electric displacement, and those associated with electric quadrupole densities exhibit the weaker r − 1 / 2 singularity near the crack tip.