Closed-form solution for elliptical inclusion problem in antiplane piezoelectricity with far-field loading at an arbitrary angle

An elliptical piezoelectric inclusion embedded in an infinite piezoelectric matrix is analyzed in the framework of linear piezoelectricity. Using the conformal mapping technique, a closed-form solution is obtained for the case of a far-field antiplane mechanical load, τ0, and an inplane electrical load, E0, at an arbitrary angle β. The stress and electric field distribution patterns for different defect shapes, loading angles, and material constants are studied. The energy release rates of self-similarly expanding and rotating defects in the presence of an electric field are obtained using the generalized M- and L-integrals as a function of the loading angle. The physical significance of these results is discussed in terms of the stress and electric field distributions as well as the energy release rates.