Stress fields and effective modulus of piezoelectric fiber composite with arbitrary shaped inclusion under in-plane mechanical and anti-plane electric loadings

The piezoelectric fiber composite, which has been widely used in vibration control of aeronautic and aerospace structures, contains an active layer constructed by piezoceramic fibers embedded in polymer matrix. In this paper, an analytical framework is developed to predict the stress fields and the effective elastic and piezoelectric modulus of a piezoelectric fiber composite with arbitrary shaped inclusion under in-plane mechanical and anti-plane electric loadings. Firstly, a three-phase model is presented based on the general self-consistent method. It assumes that a representative volume element, consisting of an arbitrary shaped piezoelectric fiber and non-piezoelectric matrix, is embedded in infinite equivalent medium of piezoelectric fiber composite. Also, in order to obtain the complex potentials in different phases, a new conformal mapping method is proposed to translate two arbitrary connected domains into an annular domain. Then, the general solution of each complex potential can be expressed in series form with some coefficients. The continuity conditions of the interfaces and the homogeneous conditions are used to build up a set of equations to determine the coefficients. After the complex potentials are solved, the exact stress responses and effective modulus of piezoelectric fiber composite with arbitrary shaped inclusion are obtained. It is shown that the piezoelectric fiber shape and volume fraction have significant influence on the stress distributions around the piezoelectric fiber and effective modulus of the piezoelectric fiber composite. Furthermore, the proposed analytical framework provides a powerful instrument for solving related problems about fiber-reinforced composites with imperfect interface or with coated phase.