A generalized and mathematically rigorous model is developed to treat the partially-debonded circular inhomogeneity problem in piezoelectric materials under antiplane shear and in plane electric field using the complex variable method. The principle of analytical continuation and the complex series expansion method were employed to reduce the formulations into Riemann Hilbert problems. This enabled the explicit determination of the complex potentials inside the inhomogeneity and the matrix. The resulting closed form expressions were then used to obtain the energy release rate for several interesting cases involving partial-debonding at the inhomogeneity-matrix interface.

This paper studies a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains. The analytical elastic solution is obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructural parameters and its evolution on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated through examples.

In this paper we studied a finite crack in an infinite medium made of a functionally gradient piezoelectric material subjected to antiplane shear and inplane electric field. The material properties, including the elastic shear modulus, the piezoelectric modulus and the dielectric modulus are assumed to vary exponentially with spatial position. By means of Fourier transformation, the governing equations of the problem are firstly reduced to two pairs of dual integral equations and then to a Fredholm integral equation of second kind. The electroelastic fields are completely determined and the field intensity factors can be defined. It is found that the stress and the electric displacement have the inverse square-root singularity at the crack tip as that of homogeneous piezoelectric materials, and the stress intensity factor and the electric displacement intensity factor increase with the increase of the material gradient constant of functionally gradient piezoelectric materials.