Piezoelectric study on singularities interacting with interfaces in an anisotropic media

In this work, the singularity problem of a three-phase anisotropic piezoelectric media is studied using the extended Stroh formalism. Based on the method of analytical continuation in conjunction with alternating technique, the general expressions for the complex potentials are derived in each medium of a three-phase anisotropic piezoelectric media. This approach has a clear advantage in deriving the solution to the heterogeneous problem in terms of the solution for the corresponding homogeneous problem. The presented series solutions have rapid convergence which is guaranteed numerically. Stress and electric fields which are dependent on the mismatch in the material constants, the location of singularities and the magnitude of electromechanical loadings are studied in detail. Numerical results demonstrate that the continuity conditions at the interfaces are indeed satisfied and show the effects of material mismatch on the stress and electric displacement fields. The image forces exerted on a dislocation due to the interfaces are also calculated by means of the generalized Peach–Koehler formula.