Abstract
Scattering cross-sections are calculated for a crack in three-dimensional elastic solids. The crack opening displacements are evaluated first by the boundary element methods. Then the scattering amplitudes for the crack are derived from the far-field representations of the scattered fields. In the final step to calculate the scattering cross-sections from scattering amplitudes, two methods are compared. One is the method based on the definition and here the scattering cross-section is calculated from the integration of the differential cross-sections over the solid angle. The other is the method based on the elastodynamic counterpart of the optical theorem. It is verified that the results obtained from the elastodynamic optical theorem are accurate enough to evaluate the scattering cross-section for the crack in elastic solids.
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References
P.J. Barratt and W.D. Collins, Proc. Camb. Phil. Soc. 61, 969 (1965).
J.E. Gubernatis, E. Domany and J.A. Krumhansl, J. Appl. Phys. 48, 2804 (1977).
A.I. Beltzer, Wave Motion 11, 211 (1989).
S.M. Nair, D.K. Hsu and J.H. Rose, J. Nondestructive Evaluation 8, 13 (1989).
S. Krenk and H. Schmidt, Phil. Trans. R. Soc. Lond. A308, 167 (1982).
P.A. Martin and G.W. Wickham, Proc. R. Soc. Lond. A390, 91 (1983).
N. Nishimura and S. Kobayashi, in Advanced Boundary Element Methods, ed. T.A. Cruse(Springer-Verlag, Berlin Heidelberg, 1988), p.279.
D.E. Budreck and J.D. Achenbach, J. Appl. Mech. 55, 405 (1988).
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Kitahara, M., Nakagawa, K. (1997). Elastodynamic Optical Theorem for the Evaluation of Scattering Cross-Sections for a Crack. In: Thompson, D.O., Chimenti, D.E. (eds) Review of Progress in Quantitative Nondestructive Evaluation. Review of Progress in Quantitative Nondestructive Evaluation, vol 16. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5947-4_4
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DOI: https://doi.org/10.1007/978-1-4615-5947-4_4
Publisher Name: Springer, Boston, MA
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