Effects of nonhomogeneity on singular electroelastic field near electrodes for a functionally graded piezoelectric material

Functionally graded piezoelectric material (FGPM) has attracted great attention as sensors and actuators due to its improved reliability and performance. This paper aims at the study of fracture behavior relating to FGPM. In this paper, electroelastic field concentration near electrodes for a FGPM under anti-plane shear deformation is obtained. The Fourier transform technique is applied to reduce the boundary value problem to a pair of dual integral equations, and then to singular integral equation with Cauchy kernel. The resulting singular integral equations are solved by Lobatto-Chebyshev quadrature method. The field intensity factors such as electric displacement and stress intensity factors have been obtained numerically. The influences of nonhomogeneity and geometry parameters on the field intensity factors have been discussed. Theoretical analysis reveals a linear relationship between stress intensity factors and the electric displacement intensity factors. Moreover, the nonhomogeneous parameter should be properly selected to balance the intensity factors on the top and bottom surface electrodes.