Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by ellipsoidal inclusions

The magneto-electro-elastic Eshelby tensors that represent the stress, electric displacement, and magnetic induction in an inclusion resulting from the constraint of the surrounding matrix of piezomagnetic-piezoelectric composites are presented. The tensors provide the basis for analysis of the magneto-electro-elastic response of the composites and have numerous applications such as to the study of defects, overall properties of multiphase composites, and fracture mechanics, etc. For a three-dimensional transversely isotropic piezoelectric/piezomagnetic composite containing spheriodal inclusions, the number of nonzero Eshelby tensors is 41 while among them only 17 are independent. These independent tensors can be divided into three categories. The first category consists of those tensors related to the elastic response, the second involves those related to the piezomagnetic response, while the third includes elastic and magnetic interactive terms. Moreover, the magneto-electro-elastic Eshelby tensors are obtained in the closed forms when both constituents of the composite are transversely isotropic and shapes of the inclusion are elliptic, rod shaped, penny shaped, and ribbon like.