Electroelastic fields in interacting piezoelectric inhomogeneities by the electromechanicalequivalent inclusion method

Abstract

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