Summary: The problem of interactions between an inclusion and multiple cracks in a thermopiezoelectric solid is examined by boundary element method (BEM). First of all, a BEM for the crack-inclusion problem is developed by way of potential variational principle, the concept of dislocation, and Green’s function. In the BE model, the continuity condition on the interface between inclusion and matrix is satisfied a priori by the Green’s function, and is not involved in the boundary element equations. This is then followed by expressing stress and electric displacements (SED) and elastic displacements and electric potential in terms of polynomials of complex variables \(\xi_t\) and \(\xi_k\) in the transformed \(\xi\)-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.

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