Electroelastic fields in interacting piezoelectric inhomogeneities by the electromechanical equivalent inclusion method

Consider two piezoelectric ellipsoidal inhomogeneities of arbitrary size, orientation and material constants, which in turn are surrounded by an infinite isotropic medium. The system under consideration is subjected to far-field non-uniform electromechanical loadings. Based on the extension of the electromechanical equivalent inclusion method (EMEIM), the present paper develops a unified solution for determination of the associated electroelastic fields in the vicinity of interacting inhomogeneities. Accordingly, each of the piezoelectric inhomogeneities is broken down into two equivalent inclusions with proper polynomial eigenstrains and eigenelectric fields. The robustness and efficacy of the present solution are demonstrated through consideration of several boundary value problems. As a special case encompassed by the presented formulation, the interaction of a piezoelectric inhomogeneity and a lamellar inhomogeneity for two- and three-dimensional problems is addressed. For a particular case involving interaction of a slit-like crack and a piezoelectric circular fiber, comparison with the other available results in the literature attests to the validity of the proposed method. Subsequently, the effect of some parameters such as geometry and stiffness of each phase on the quantitative value of stress intensity factors (SIFs) are examined for far-field non-uniform loadings.