Exact solutions of interfacial cracking problem of elliptic inclusion in thermoelectric material

Abstract

In the present work, the problem for elliptical inclusion with interfacial crack in thermoelectric material is studied. The inclusion and matrix are assumed to be imperfect bonding, which is subjected to uniform heat flux and energy flux at infinity. The interfacial cracking problem of elliptic inclusion in thermoelectric material is investigated by using conformal mapping and complex function method. The complex expressions of temperature field and electric field in inclusion and matrix are obtained. The energy release rate of thermoelectric material under the influence of inclusion is given. The effects of elliptic inclusion with interfacial crack on temperature field and electric potential also are compared by numerical examples. The results show that inclusion reduces the conversion efficiency of thermoelectric material.