SOLUTIONS FOR DYNAMIC VARIANTS OF ESHELBY’S INCLUSION PROBLEM

  • Thomas M. Michelitsch
  • Harm Askes
  • Jizeng Wang
  • Valery M. Levin
Part of the Springer Proceedings in Physics book series (SPPHY, volume 111)

Abstract

The dynamic variant of Eshelby’s inclusion problem plays a crucial role in many areas of mechanics and theoretical physics. Because of its mathematical complexity, dynamic variants of the inclusion problems so far are only little touched. In this paper we derive solutions for dynamic variants of the Eshelby inclusion problem for arbitrary scalar source densities of the eigenstrain. We study a series of examples of Eshelby problems which are of interest for applications in materials sciences, such as for instance cubic and prismatic inclusions. The method which covers both the time and frequency domain is especially useful for dynamically transforming inclusions of any shape.

Keywords

Convolution Acoustics 

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References

  1. Eshelby J. D. (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. Lond. A 241 376–396.MathSciNetADSMATHCrossRefGoogle Scholar
  2. Levin V. M., Michelitsch T. M., Gao H. (2002) Propagation of electroacoustic waves in the transversely isotropic piezoelectric medium reinforced by randomly distributed cylindrical inhomogeneities, Int. J. Solids Structures 39 5013–5051.CrossRefMATHGoogle Scholar
  3. Michelitsch T. M., Levin V. M., Gao H. (2002c) Dynamic potentials and Green's functions of a quasi-plane piezoelectric medium with inclusion, Proc. Roy. Soc. Lond. A 458 2393–2415.MathSciNetADSCrossRefMATHGoogle Scholar
  4. Michelitsch T. M., Levin V. M., Gao H. (2003) Dynamic Eshelby tensor and potentials for ellipsoidal inclusions, Proceedings of the Royal Society of London A 459 863–890.MathSciNetADSMATHCrossRefGoogle Scholar
  5. Mikata Y., Nemat-Nasser S. (1990) Elastic field due to a Dynamically Transforming Spherical Inclusion, J. Appl. Mech. ASME 57 845–849.MATHCrossRefGoogle Scholar
  6. Press W. H., Teukolsky S. A, Vetterling W. T., Flannery, B. P. (1992) Numerical Recipes in Fortran 77: the Art of Scientific Computing (Second Edition), Cambridge University Press.Google Scholar
  7. Pao Y. H. (Ed.) (1978) Elastic Waves and non-destructive testing of materials, AMD-Vol. ASME 29.Google Scholar
  8. Wang J., Michelitsch T. M., Gao H., Levin V. M. (2005) On the solution of the dynamic Eshelby problem for inclusions of various shapes, International Journal of Solids and Structures 42 353–363.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Thomas M. Michelitsch
    • 1
  • Harm Askes
    • 1
  • Jizeng Wang
    • 2
  • Valery M. Levin
    • 3
  1. 1.Department of Civil and Structural EngineeringThe University of SheffieldSheffieldUnited Kingdom
  2. 2.Max-Planck Institute for Metals ResearchStuttgartGermany
  3. 3.Instituto Mexicano del PetroleoMexico

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