An ellipsoidal inclusion and an elliptical crack in the elastic media with ellipsoidal anisotropy

Abstract

An isolated ellipsoidal inclusion and an elliptical crack in a homogeneous elastic medium with ellipsoidal anisotropy are considered. For constant external stress (strain) fields applied to the medium, the solutions of these problems are reduced to calculation of 2D-regular integrals. For materials with ellipsoidal anisotropy, the integrand functions in these integrals can be presented in explicit analytical forms that simplifies substantially construction of the numerical solutions of the problems. The stress intensity factors at the crack edge are expressed in the forms of 1D-integrals which integrand functions have also explicit analytical forms for media with ellipsoidal anisotropy.

This is a preview of subscription content, access via your institution.

References

  1. Kanaun S (2007) Elliptical crack in an anisotropic elastic medium subjected with a constant external field. Int J Fract 148:95–102

    Article  Google Scholar 

  2. Kanaun S, Levin V (2008) Self-consistent methods for composites, vol 1. Static problems. Springer, Dordrecht

    Google Scholar 

  3. Kanaun S, Levin V (2009) Elliptical cracks arbitrary oriented in 3D-anisotropic elastic media. Int J Eng Sci 47:777–792

    Article  Google Scholar 

  4. Kunin I (1983) The theory of elastic media with microstructure, vol 2. Springer, Berlin

    Google Scholar 

  5. Pouya A (2011) Ellipsoidal anisotropy in linear elasticity: approximation models and analytical solutions. Int J Solids Struct 48:2245–2254

    Article  Google Scholar 

  6. Willis J (1968) The stress field around an elliptical crack in an anisotropic medium. Int J Eng Sci 6:253–263

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to S. Kanaun.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kanaun, S. An ellipsoidal inclusion and an elliptical crack in the elastic media with ellipsoidal anisotropy. Int J Fract 227, 133–136 (2021). https://doi.org/10.1007/s10704-020-00498-4

Download citation

Keywords

  • Ellipsoidal anisotropy
  • Ellipsoidal inclusion
  • Elliptical crack
  • Stress intensity factors