Skip to main content
SpringerLink
Log in

Uniform elastic field within an imperfectly bonded isotropic or anisotropic ellipsoidal inhomogeneity

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

We establish the uniformity of stresses and strains inside an imperfectly bonded elastic ellipsoidal inhomogeneity embedded within an infinite elastic matrix subjected to uniform remote stresses and strains. Both the inhomogeneity and the matrix can be either isotropic elastic or generally anisotropic elastic. The imperfect interface is described by a spring-type imperfect interface characterized by a single imperfect interface function. The same degree of imperfection of the ellipsoidal interface is realized in both the normal and tangential directions. We identify the imperfect interface function leading to an internal uniform field. The internal uniform strains and stresses within the ellipsoidal inhomogeneity are obtained with the aid of Eshelby’s equivalent inclusion method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

The authors are grateful to the editor and an anonymous reviewer for useful comments which have improved the manuscript.

References

  1. Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A 241, 376–396 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  2. Eshelby, J.D.: The elastic field outside an ellipsoidal inclusion. Proc. R. Soc. Lond. A 252, 561–569 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  3. Eshelby, J.D.: Elastic inclusions and inhomogeneities. Prog. Solid Mech. 2, 89–140 (1961)

    MathSciNet  Google Scholar 

  4. Hashin, Z.: Thermoelastic properties of particulate composites with imperfect interface. J. Mech. Phys. Solids 39, 745–762 (1991)

    Article  MathSciNet  Google Scholar 

  5. Gao, J.: A circular inhomogeneity with imperfect interface: Eshelby’s tensor and related problems. ASME J. Appl. Mech. 62, 860–866 (1995)

    Article  MATH  Google Scholar 

  6. Zhong, Z., Meguid, S.A.: On the elastic field of a spherical inhomogeneity with an imperfectly bonded interface. J. Elast. 46, 91–113 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ru, C.Q., Schiavone, P.: A circular inclusion with circumferentially inhomogeneous interface in antiplane shear. Proc. R. Soc. Lond. A 453, 2551–2572 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ru, C.Q.: A circular inclusion with circumferentially inhomogeneous sliding interface in plane elastostatics. ASME J. Appl. Mech. 65, 30–38 (1998)

    Article  MathSciNet  Google Scholar 

  9. Ru, C.Q.: Interface design of neutral elastic inclusions. Int. J. Solids Struct. 35, 559–572 (1998)

    Article  MATH  Google Scholar 

  10. Shilkrot, L.E., Srolovitz, D.J.: Elastic analysis of finite stiffness bimaterial interfaces: application to dislocation-interface interactions. Acta Mater. 46(9), 3063–3075 (1998)

    Article  Google Scholar 

  11. Shen, H., Schiavone, P., Ru, C.Q., Mioduchowski, A.: An elliptic inclusion with imperfect interface in anti-plane shear. Int. J. Solids Struct. 37, 4557–4575 (2000)

    Article  MATH  Google Scholar 

  12. Fan, H., Wang, G.F.: Screw dislocation interacting with imperfect interface. Mech. Mater. 35, 943–953 (2003)

    Article  Google Scholar 

  13. Antipov, Y.A., Schiavone, P.: On the uniformity of stresses inside an inhomogeneity of arbitrary shape. IMA J. Appl. Math. 68, 299–311 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, X., Sudak, L.J., Ru, C.Q.: Elastic fields in two imperfectly bonded half-planes with a thermal inclusion of arbitrary shape. Z. Angew. Math. Phys. 58, 488–509 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, X., Pan, E., Sudak, L.J.: Uniform stresses inside an elliptical inhomogeneity with an imperfect interface in plane elasticity. ASME J. Appl. Mech. 75, 054501 (2008)

    Article  Google Scholar 

  16. Mura, T.: Micromechanics of Defects in Solids, 2nd rev. edn. Martinus Nijhoff, Dordrecht (1987)

    Book  MATH  Google Scholar 

Download references

Funding

This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No.: RGPIN-2023-03227 Schiavo).

Author information

Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China

    Xu Wang

  2. Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, AB , T6G 1H9, Canada

    Peter Schiavone

Authors
  1. Xu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Schiavone
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Both authors wrote and reviewed the manuscript.

Corresponding authors

Correspondence to Xu Wang or Peter Schiavone.

Ethics declarations

Competing interests

The authors declare that they have no competing interests.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Schiavone, P. Uniform elastic field within an imperfectly bonded isotropic or anisotropic ellipsoidal inhomogeneity. Z. Angew. Math. Phys. 74, 185 (2023). https://doi.org/10.1007/s00033-023-02071-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00033-023-02071-0

Keywords

Mathematics Subject Classification

Search

Navigation