Abstract
Recently Fu and Mielke uncovered a new identity that the surface impedance tensor of any anisotropic elastic material has to satisfy. By solving algebraically a matrix equation that follows from the new identity, we derive an explicit expression for the surface impedance tensor, which is correct up to terms linear in the components of the anisotropic part of the elasticity tensor of the material in question. From the well-known relationship between the surface impedance tensor and the Green’s function for infinite space, we obtain an explicit expression for the Green’s function, which is correct up to terms linear in the components of the anisotropic part of the elasticity tensor.
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Tanuma, K., Man, C.-S., Huang, M., Nakamura, G.: Surface impedance tensors of textured polycrystals. J. Elast. 67, 131–147 (2002)
Barnett, D.M., Lothe, J.: Synthesis of the sextic and the integral formalism for dislocations, Green’s functions, and surface waves in anisotropic elastic solids. Phys. Norv. 7, 13–19 (1973)
Lothe, J., Barnett, D.M.: On the existence of surface-wave solutions for anisotropic elastic half-spaces with free surface. J. Appl. Phys. 47, 428–433 (1976)
Huang, M., Zheng, C.: Green’s function and effective elastic stiffness tensor for arbitrary aggregates of cubic crystals. Acta Mech. Solida Sinica 17, 337–346 (2004)
Synge, J.L.: The Hypercircle in Mathematical Physics. Cambridge University Press (1957)
Fu, Y.B., Mielke, A.: A new identity for the surface-impedance matrix and its application to the determination of surface-wave speeds. Proc. R. Soc. Lond. A458, 2523–2543 (2002)
Huang, M., Man, C.-S.: Constitutive relation of elastic polycrystal with quadratic texture dependence. J. Elast. 72, 183–212 (2003)
Roe, R.J.: Description of crystallite orientation in polycrystalline materials: III, General solution to pole figures. J. Appl. Phys. 36, 2024–2031 (1965)
Huang, M.: Perturbation approach to elastic Constitutive relations of polycrystals. J. Mech. Phys. Solids. 52, 1827–1853 (2004)
Tanuma K.: Stroh Formalism and Rayleigh Waves. J. Elast. (2007) doi:10.1007/s10659-007-9117-1
Ting, T.C.T.: Anisotropic Elasticity: Theory and Applications. Oxford Univ. Press, New York (1996)
Hoger, A., Carlson, D.E.: On the derivative of the aquare root of a tensor and Guo’s rate theorems. J. Elast. 14, 329–336 (1984)
Man, C.-S.: On the constitutive equations of some weakly-textured materials. Arch. Ration. Mech. Anal. 143, 77–103 (1998)
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Huang, M., Zhan, H., Liu, X. et al. Surface Impedance Tensor and Green’s Function for Weakly Anisotropic Elastic Materials. J Elasticity 90, 283–294 (2008). https://doi.org/10.1007/s10659-007-9144-y
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DOI: https://doi.org/10.1007/s10659-007-9144-y