A second-order theory for magnetoelectroelastic materials with transverse isotropy

In this paper, we concentrate on the basic governing equations of three-dimensional problems in transversely isotropic and nonlinear magnetoelectroelastic materials (i.e., 6 (m) under bar (m) under bar magnetic crystals). We place emphasis on developing the nonlinear and fully coupled constitutive relations between extended traction (including elastic stress, polarization and magnetization) and extended strain (including elastic strain, electric field and magnetic induction). Simplified results are also presented for the corresponding small deformation problems in the case of both strong magnetic and electric fields and in the case of both weak magnetic and electric fields. The derived concise equations are important in investigating the nonlinear magnetoelectric effects of novel magnetoelectroelastic materials.