Piezoelectric screw dislocation in an arbitrarily shaped three-phase composite

Based on the methods of complex variable, conformal mapping, Faber series and Laurent series, the Green’s function for a coated inclusion of arbitrary shape embedded in an infinite piezoelectric matrix is obtained in this paper. The analytical complex potentials for all three regions can be expressed in series form with unknown coefficients. The continuity conditions of the interfaces are used to build up a set of linear equations to determine the unknown coefficients. After the unknown coefficients are solved, the stress, electric field and image force can be expressed explicitly. Numerical results are provided to show the effect of the inclusion shape, the material combinations on the electroelastic fields and image force calculated through the generalized Peach–Koehler formula. The solutions proposed here can be served as kernel functions to analyze the corresponding piezoelectric cracking problems.