This paper is concerned with the development of a model for the treatment of a circular arc-crack in piezoelectric materials under antiplane shear and inplane electric field using the complex variable method. The problem is formulated in terms of the analytical continuation principle and complex series expansion, and as a result is reduced to two Riemann-Hilbert problems. The resulting closed form solution was then used to obtain the electroelastic field intensity factor and the energy release rate. Unlike the electric enthalpy release rate, the internal energy release rate is always positive and can thus be used as a more reliable fracture parameter in piezoelectric materials. It is also observed that the crack configuration has a significant influence upon the energy release rate.

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.