Acta Mechanica

, Volume 229, Issue 4, pp 1597–1611 | Cite as

On elastic fields of perfectly bonded and sliding circular inhomogeneities in an infinite matrix

Original Paper


The solutions to classical problems of perfectly bonded and sliding circular inhomogeneities in a remotely loaded infinite matrix are constructed by using an appealing choice of dimensionless material parameters that represent the in-plane average normal stress and the maximum shear stress at the center of the inhomogeneity, scaled by the corresponding measures of remote stress. The ovalization of the inhomogeneity and the effects of material parameters on stress concentration are discussed. The range of material parameters is specified for which the inhomogeneity with a perfectly bonded interface can expand in vertical direction under horizontal remote loading. For some combination of material properties, the maximum compressive hoop stress in the matrix along the interface can be larger than the maximum hoop stress around a circular void under tensile remote loading. The strain energies stored in perfectly bonded and sliding inhomogeneities are evaluated and discussed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen (1953)MATHGoogle Scholar
  2. 2.
    Mura, T.: Micromechanics of Defects in Solids, 2nd edn. Kluwer Academic Publishers, Dordrecht (1987)CrossRefMATHGoogle Scholar
  3. 3.
    Nemat-Nasser, S., Hori, M.: Micromechanics: Overall Properties of Heterogeneous Materials, 2nd edn. North-Holland, Amsterdam (1999)MATHGoogle Scholar
  4. 4.
    Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1970)MATHGoogle Scholar
  5. 5.
    Ugural, A.C., Fenster, S.K.: Advanced Mechanics of Materials and Applied Elasticity. Prentice Hall, Upper Saddle River (2003)MATHGoogle Scholar
  6. 6.
    Ghahremani, F.: Effect of grain boundary sliding on anelasticity of polycrystals. Int. J. Solids Struct. 16, 825–845 (1980)CrossRefMATHGoogle Scholar
  7. 7.
    Cook, R.D., Young, W.C.: Advanced Mechanics of Materials, 2nd edn. Pearson College Division, London (1999)Google Scholar
  8. 8.
    Krajcinovic, D.: Damage Mechanics. Elsevier, Amsterdam (1996)MATHGoogle Scholar
  9. 9.
    Noble, B., Hussain, M.A.: Exact solution of certain dual series for indentation and inclusion problems. Int. J. Eng. Sci. 7, 1149–1161 (1969)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Keer, L.M., Dundurs, J., Kiattikomol, K.: Separation of a smooth circular inclusion from a matrix. Int. J. Eng. Sci. 1, 1221–1233 (1973)CrossRefGoogle Scholar
  11. 11.
    Furuhashi, R., Huang, J.H., Mura, T.: Sliding inclusions and inhomogeneities with frictional interfaces. J. Appl. Mech. 59, 783–788 (1992)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Kattis, M.A., Providas, E.: Inplane deformation of a circular inhomogeneity with imperfect interface. Theor. Appl. Fract. Mech. 28, 213–222 (1998)CrossRefMATHGoogle Scholar
  13. 13.
    Honein, T., Herrmann, G.: On bonded inclusions with circular or straight boundaries in plane elastostatics. J. Appl. Mech. 57, 850–856 (1990)CrossRefMATHGoogle Scholar
  14. 14.
    Goodier, J.N.: Concentration of stress around spherical and cylindrical inclusions and flaws. J. Appl. Mech. 55, 39–44 (1933)Google Scholar
  15. 15.
    Dundurs, J.: Effect of elastic constants on stress in a composite under plane deformation. J. Compos. Mater. 1, 310–322 (1967)CrossRefGoogle Scholar
  16. 16.
    Malvern, L.E.: Introduction to the Mechanics of Continuous Media. Prentice Hall, Upper Saddle River (1968)Google Scholar
  17. 17.
    Mura, T., Jasiuk, I., Tsuchida, E.: The stress field of a sliding inclusion. Int. J. Solids Struct. 21, 1165–1179 (1985)CrossRefGoogle Scholar
  18. 18.
    Lubarda, V.A.: Sliding and bonded circular inclusions in concentric cylinders. Proc. Monten. Acad. Sci. Arts OPN 12, 123–139 (1998)Google Scholar
  19. 19.
    Lubarda, V.A., Markenscoff, X.: Energies of circular inclusions: sliding versus bonded interfaces. Proc. R. Soc. Lond. A 455, 961–974 (1999)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Lee, M., Jasiuk, I., Tsuchida, E.: The sliding circular inclusion in an elastic half-plane. J. Appl. Mech. 59, S57–S64 (1992)CrossRefMATHGoogle Scholar
  21. 21.
    Stagni, L.: On the elastic field perturbation by inhomogeneities in plane elasticity. J. Appl. Math. Phys. 33, 315–325 (1982)CrossRefMATHGoogle Scholar
  22. 22.
    Tsuchida, E., Mura, T., Dundurs, J.: The elastic field of an elliptic inclusion with a slipping interface. J. Appl. Mech. 53, 103–107 (1986)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Jasiuk, I., Tsuchida, E., Mura, T.: The sliding inclusion under shear. Int. J. Solids Struct. 23, 1373–1385 (1987)CrossRefMATHGoogle Scholar
  24. 24.
    Lubarda, V.A., Markenscoff, X.: On the stress field in sliding ellipsoidal inclusions with shear eigenstrain. J. Appl. Mech. 65, 858–862 (1998)CrossRefGoogle Scholar
  25. 25.
    Lubarda, V.A., Markenscoff, X.: On the absence of Eshelby property for ellipsoidal inclusions. Int. J. Solids Struct. 35, 3405–3411 (1998)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Lubarda, V.A.: On the circumferential shear stress around circular and elliptical holes. Arch. Appl. Mech. 85, 223–235 (2015)CrossRefGoogle Scholar
  27. 27.
    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)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Christensen, R.M.: Mechanics of Composite Materials. Wiley, New York (1980)Google Scholar
  29. 29.
    Voyiadjis, G.Z., Kattan, P.I.: Mechanics of Composite Materials with MATLAB. Springer, Berlin (2005)Google Scholar
  30. 30.
    Asaro, R.J., Lubarda, V.A.: Mechanics of Solids and Materials. Cambridge University Press, Cambridge (2006)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  1. 1.Department of NanoEngineeringUniversity of California, San DiegoLa JollaUSA

Personalised recommendations