Anti-plane electro-elastic fields in an infinite matrix with N coated-piezoelectric inclusions

Electro-elastic fields in an infinite matrix with N coated-piezoelectric inclusions are studied based on the complex variable method. Based on the assumption that the coated inclusions are completely bounded the matrix which is subjected to remote anti-plane shears and in-plane electric fields, the general solutions for complex potentials are first derived for arbitrary arrays of inclusions. Then, the numerical results are obtained for special cases in which the inclusions are located in different ways. Discussions are made about the influence of the coating thickness, the array type of inclusions and the material properties on the interface stresses and electric displacements in the matrix. It is found that both the array types of inclusions and the Young's modulus of the three-phase material system have remarkable effects on stresses, but not on electric displacements, while the piezoelectric constants of the coating and its thickness have significant effects on electric displacements, but not on stresses.