BEM for crack-inclusion problems of plane thermopiezoelectric solids

The problem of interactions between an inclusion and multiple cracks in a thermopiezoelectric solid is considered by boundary element method (BEM) in this paper. First of all, a BEM for the crack}inclusion problem is developed by way of potential variational principle, the concept of dislocation, and Greenʹs function. In the BE model, the continuity condition of the interface between inclusion and matrix is satis"ed, a priori, by the Greenʹs function, and not involved in the boundary element equations. This is then followed by expressing the stress and electric displacement (SED) and elastic displacements and electric potential (EDEP) in terms of polynomials of complex variables mt and mk in the transformed m-plane in order to simulate SED intensity factors by the BEM. The least-squares method incorporating the BE formulation can, then, be used to calculate SED intensity factors directly. Numerical results for a piezoelectric plate with one inclusion and a crack are presented to illustrate the application of the proposed formulation