On the structure and invariance of the Barnett-Lothe tensors
Authors:
P. Chadwick and T. C. T. Ting
Journal:
Quart. Appl. Math. 45 (1987), 419-427
MSC:
Primary 73C20; Secondary 73D99
DOI:
https://doi.org/10.1090/qam/910450
MathSciNet review:
910450
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Abstract: The three real tensors introduced by Barnett and Lothe into the theory of steady plane motions of an anisotropic elastic body are shown to have algebraic representations the structure of which is largely independent of material symmetry. The allied form of the complex impedance tensor central to the analyses of surface and interfacial waves in anisotropic elastodynamics is also obtained. A detailed study of the representations yields alternative routes to known results and a variety of new relations. The paper concludes with a discussion of the invariance properties of quantities appearing in the representations under rotations of the reference frame about the direction in which the deformation is uniform.
D. M. Barnett and J. Lothe, Synthesis of the sextic and integral formalism for dislocations, Greens functions and surface waves in anisotropic elastic solids, Phys. Norv. 7, 13–19 (1973)
K. A. Ingebrigtsen and A. Tonning, Elastic surface waves in crystals, Phys. Rev. 184, 942–951 (1969)
P. Chadwick and G. D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, Advances in Applied Mechanics (Ed. C.-S. Yih), Vol. 17, Academic Press, New York, 303–376, 1977
- D. M. Barnett and J. Lothe, Free surface (Rayleigh) waves in anisotropic elastic half-spaces: the surface impedance method, Proc. Roy. Soc. London Ser. A 402 (1985), no. 1822, 135–152. MR 819916
- T. C. T. Ting, Explicit solution and invariance of the singularities at an interface crack in anisotropic composites, Internat. J. Solids Structures 22 (1986), no. 9, 965–983. MR 865545, DOI https://doi.org/10.1016/0020-7683%2886%2990031-4
- P. Chadwick, Continuum mechanics, Halsted Press [John Wiley & Sons], New York, 1976. Concise theory and problems. MR 0388914
- P. Chadwick and D. A. Jarvis, Surface waves in a prestressed elastic body, Proc. Roy. Soc. London Ser. A 366 (1979), no. 1727, 517–536. MR 547761, DOI https://doi.org/10.1098/rspa.1979.0067
D. M. Barnett, J. Lothe, K. Nishioka, and R. J. Asaro, Elastic surface waves in anisotropic crystals: A simplified method for calculating Rayleigh velocities using dislocation theory, J. Phys. F. 3, 1083–1096 (1973)
- P. Chadwick and G. D. Smith, Surface of waves in cubic elastic materials, Mechanics of solids, Pergamon, Oxford-Elmsford, N.Y., 1982, pp. 47–100. MR 652695
- T. C. T. Ting, Effects of change of reference coordinates on the stress analyses of anisotropic elastic materials, Internat. J. Solids Structures 18 (1982), no. 2, 139–152. MR 639099, DOI https://doi.org/10.1016/0020-7683%2882%2990022-1
H. O. K. Kirchner and J. Lothe, On the redundancy of the $\bar N$ matrix of anisotopic elasticity, Phil. Mag. A53, L7–L10 (1986)
D. M. Barnett and J. Lothe, Synthesis of the sextic and integral formalism for dislocations, Greens functions and surface waves in anisotropic elastic solids, Phys. Norv. 7, 13–19 (1973)
K. A. Ingebrigtsen and A. Tonning, Elastic surface waves in crystals, Phys. Rev. 184, 942–951 (1969)
P. Chadwick and G. D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, Advances in Applied Mechanics (Ed. C.-S. Yih), Vol. 17, Academic Press, New York, 303–376, 1977
D. M. Barnett and J. Lothe, Free surface (Rayleigh) waves in anisotropic elastic half-spaces: the surface impedance method, Proc. Roy. Soc. Lond. A402, 135–152 (1985)
T. C. T. Ting, Explicit solution and invariance of the singularities at an interface crack in anisotropic composites, Internat. J. Solids and Structures 22, 965–983 (1986)
P. Chadwick, Continuum mechanics. Concise theory and problems, Allen & Unwin, London, 1976
P. Chadwick and D. A. Jarvis, Surface waves in a prestressed elastic body, Proc. Roy. Soc. Lond. A366, 517–536 (1979)
D. M. Barnett, J. Lothe, K. Nishioka, and R. J. Asaro, Elastic surface waves in anisotropic crystals: A simplified method for calculating Rayleigh velocities using dislocation theory, J. Phys. F. 3, 1083–1096 (1973)
P. Chadwick and G. D. Smith, Surface waves in cubic elastic materials. Mechanics of Solids, The Rodney Hill 60th Anniversary Volume (eds, H. G. Hopkins and M. J. Sewell), Pergamon, Oxford, 47–100, 1982
T. C. T. Ting, Effects of change of reference coordinates on the stress analyses of anisotropic elastic materials, Internat. J. Solids and Structures 18, 139–152 (1982)
H. O. K. Kirchner and J. Lothe, On the redundancy of the $\bar N$ matrix of anisotopic elasticity, Phil. Mag. A53, L7–L10 (1986)
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Article copyright:
© Copyright 1987
American Mathematical Society
