Dynamic potentials and Green’s functions of a quasi-plane magneto-electro-elastic medium with inclusion

The dynamic potentials of a quasi-plane magneto-electro-elastic medium of transversely isotropic symmetry with an inclusion of arbitrary shape are derived, and the dynamic potentials are finally governed by six scalar equations which can be regarded as inhomogeneous wave equations, Laplace and Helmholtz equations. The explicit expressions of the dynamic Green’s functions of this medium are also obtained both in the space–time domain and in the space–frequency domain. Closed-form expressions for the space–frequency representation of the dynamic potentials are given for the case when the inclusion is circular. The results are employed to obtain the generalized displacement fields of a circular inclusion undergoing uniform eigenstrain, eigenelectric field and eigenmagnetic field. In contrast to the corresponding static Eshelby inclusion problem the magneto-electro-elastic fields (i.e. strain, electric and magnetic field) inside the inclusion are non-uniform in the space–frequency domain.