Green´s function for an electrically permeable crack in thermopiezoelectric materials

The generalized 2D problem of thermopiezoelectric materials containing an electrically permeable crack under thermal-mechanical loading is studied in this paper. Based on the Stroh formalism and Green´s function method, the problem is reduced to a set of singular integral equations which are solved in closed-form. When the crack is assumed to be traction free, the crack opening displacement must be negative between one half of the crack faces unless a sufficiently large tensile stress is superposed. Then, Green´s function of the stress and electric displacement intensity factors at each crack tip are obtained. These results can be directly applied to the fracture analysis of piezoelectric materials in engineering applications if the crack interior is filled with conductive media.