On the generalized Barnett–Lothe tensors for anisotropic magnetoelectroelastic materials

The three generalized Barnett–Lothe tensors L, S and H are frequently encountered in the extended Stroh formalism of two-dimensional deformation of anisotropic magneto-electro-elastic materials. Meantime, they are directly related to the admittance matrix Y, which is required to characterize the crack-tip field. In this paper, the elements of L, S and H together with Y are constructed using a modified Lekhinitskii formalism for general anisotropic magneto-electro-elastic materials. As a typical case, the three generalized Barnett–Lothe tensors are explicitly expressed in terms of the reduced generalized elastic compliances for transversely isotropic magneto-electro-elastic materials. A simple example is presented to validate these expressions.