On the Barnett–Lothe tensors for anisotropic elastic materials

The three Barnett–Lothe tensors L, S and H, appearing frequently in the investigations of the two-dimensional deformations of anisotropic elastic materials, are mostly expressed explicitly in terms of the reduced elastic compliance in the literature. Only the tensor H presented by Ting [Ting, T.C.T., 1997. New explicit expression of Barnett–Lothe tensors for anisotropic linear elastic materials. J. Elasticity 47, 23–50] is expressed in terms of both elastic stiffness and reduced elastic compliance. In this paper, new expressions of the three Barnett–Lothe tensors L, S and H are all expressed explicitly in terms of the elastic stiffness for general anisotropic materials. Results for the special cases of monoclinic materials with a plane of symmetry at x3=0, x2=0, and x1=0 are all deduced. The special case of orthotropic materials expressed in terms of elastic stiffness in the literature may be recovered from present general results.