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In this study, a rigid line inclusion on the interface between two dissimilar thermo-electro-magneto-elastic solids is considered. Based on the Muskhelishvili’s theory and extended Stroh formalism, it is reduced to the non-homogeneous Hilbert equation. According to the holomorphic continuation technology and Muskhelishvili’s theory, the exact solutions for both thermal and electro-magneto-elastic fields are derived. The explicit expressions of the multiple coupling fields are presented, and the generalized stress intensity factors are illustrated with the closed form. From the results, it can be observed the coupling of the thermo-electro-magneto-elastic effects. Moreover, the generalized stress has singularities and oscillatory properties near the inclusion tip.

Two fundamental theories are discussed in this paper. In the nonlinear electro–magneto–elastic analysis, different authors give different formulas. It means that the fundamental theory should still be studied. In this paper, we give a review of different theories and extend the physical variational principle to the material with electromagnetic body couple. For the temperature wave, we compare the inertial entropy theory and the Cattaneo–Vernotte’s theory in detail and show that the former is more appropriate. These theories may be interesting and need further research.