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On the method of equivalent inclusions in elastodynamics and the scattering fields of two ellipsoidal inhomogeneities

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Abstract

Gurtin's variational principle is used to derive the equivalence equations for general linear elastodynamical problems of multiple inhomogeneities. An approximate expression on scattering field of two ellipsoidal inhomogeneities is obtained by the method of equivalent inclusions. And some numerical examples are presented.

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References

  1. Ying, C. F., R. Truell, Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid,J. App. Phys.,27, 9 (1956), 1086–1097.

    Google Scholar 

  2. Einspruch, N. G., E. J. Witterholt, R. Truell, Scattering of a plane transverse wave by a spherical obstacle in an elastic medium,J. App. Phys.,31, 5 (1960), 806–818.

    Google Scholar 

  3. Johnson, G., R. Truel, Numerical computations of elastic scattering cross section,J. App. Phys. 36, 11 (1965), 3466–3475.

    Google Scholar 

  4. Mal, A. K., L. Knopoff, Elastic wave velocities in two-component systems,J. Inst. Math. Applics.,3 (1967), 376–387.

    Google Scholar 

  5. Gubernatis, J. E., E. Domang, J. A. Krumhansl, Formal aspects of the theory of the scattering of ultrasound by flaws in elastic materials,J. App. Phys.,48, 7 (1977), 2804–2811.

    Google Scholar 

  6. Gubernatis, J. E., E. Domany, J. A. Krumhansl, M. Huberman, The born approximation in the theory of the scattering of elastic waves by flaws,J. App. Phys. 48, 7 (1977), 2812–2819.

    Google Scholar 

  7. Wheeler, P., T. Mura, Dynamic equivalence of composite material and eigenstrain problems,J. App. Mechanics, ASME,40 (1973), 498–502.

    Google Scholar 

  8. Fu, L. S., T. Mura, The determination of elastodynamic fields of an ellipsoidal inhomogeneity,J. App. Mechanics, ASME,50 (1983), 390–396.

    Google Scholar 

  9. Zhong Wei-fang, Lu Gong-fu The elastodynamical problems of two ellipsoidal inhomogeneities by the method of equivalent inclusions, Master Dissertation, Huazhong University of Science and Technology (1984).

  10. Li Hao, Zhong Wei-fang, Li Gong-fu, Evaluating volume integrals associated with elastodynamics problems of inhomogeneities by potential theory. (to be published)

  11. Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems,Proceedings of the Royal Society, London,241 (1957).

  12. Moschovidis, Z. A., T. Mora, Two-ellipsoidal inhomogeneities by the equivalent inclusion method,ASME J. App. Mechanics,42 (1975), 847–852.

    Google Scholar 

  13. Gurtin, M. E., Variational principles for linear elastodynamics,Archire for Rational Mechanics and Analysis,16, 1 (1964), 34.

    Google Scholar 

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Hao, L., Wei-fang, Z. & Gong-fu, L. On the method of equivalent inclusions in elastodynamics and the scattering fields of two ellipsoidal inhomogeneities. Appl Math Mech 6, 511–521 (1985). https://doi.org/10.1007/BF01876391

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