Prestressed and prepolarized piezoelectric material with an elliptical hole

Abstract In this paper, the antiplane state problem of an elliptic hole in a prestressed and prepolarized piezoelectric material loaded by constant, uniform remote shear stresses was performed. A compact and elementary form solution of the problem is obtained utilizing the conformal mapping technique and representation of the incremental stress and electrical fields by complex potentials. Using the boundary conditions, the coefficients of complex potentials developed as Laurent series, for the case of a piezoelectric material of class $$\bar{4}2m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> , and implicitly the components of incremental stress and electric displacement fields are obtained in a final compact and closed form.