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....

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Bibliographic Details
Published in:European journal of mechanics, A, Solids A, Solids, 2008-11, Vol.27 (6), p.1140-1160
Main Authors: Liou, J.Y., Sung, J.C.
Format: Article
Language:English
Subjects:
Anisotropic elasticity
Barnett–Lothe tensors
Monoclinic materials
Orthotropic materials
Stroh formalism
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Summary: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 x 3 = 0 , x 2 = 0 , and x 1 = 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.
ISSN:0997-7538
1873-7285
DOI:10.1016/j.euromechsol.2007.11.013