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A partially debonded circular elastic inhomogeneity with an incompressible liquid inclusion occupying the debonded section

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Abstract

We study the plane strain problem associated with a circular isotropic elastic inhomogeneity partially debonded from an infinite isotropic elastic matrix subjected to uniform remote in-plane stresses. The debonded portion of the circular interface is occupied by an incompressible liquid inclusion. A closed-form solution to the problem is derived by solving a Riemann-Hilbert problem with discontinuous coefficients and by imposing the incompressibility condition of the liquid inclusion. An elementary explicit expression for the internal uniform hydrostatic tension within the liquid inclusion is obtained. A hydrostatic far-field load will not induce any singular stress field and the entire circular interface remains perfect.

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References

  1. Erdogan, F.: Stress distribution in a nonhomogeneous elastic plane with cracks. ASME J. Appl. Mech. 30, 232–236 (1963)

    Article  ADS  Google Scholar 

  2. England, A.H.: A crack between dissimilar media. ASME J. Appl. Mech. 32, 400–402 (1965)

    Article  ADS  Google Scholar 

  3. Rice, J.R., Sih, G.C.: Plane problems of cracks in dissimilar media. ASME J. Appl. Mech. 32, 418–423 (1965)

    Article  ADS  Google Scholar 

  4. Clements, D.L.: A crack between dissimilar anisotropic media. Int. J. Eng. Sci. 9, 257–265 (1971)

    Article  Google Scholar 

  5. Willis, J.R.: Fracture mechanics of interfacial cracks. J. Mech. Phys. Solids 19, 353–368 (1971)

    Article  ADS  Google Scholar 

  6. Rice, J.R.: Elastic fracture mechanics concepts for interfacial cracks. ASME J. Appl. Mech. 55, 98–103 (1988)

    Article  ADS  Google Scholar 

  7. Suo, Z.: Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. Royal Soc. London A 427, 331–358 (1990)

    MathSciNet  CAS  ADS  Google Scholar 

  8. Gao, H.J., Abbudi, M., Barnett, D.M.: On interfacial crack-tip field in anisotropic solids. J. Mech. Phys. Solids 40, 393–416 (1992)

    Article  CAS  ADS  Google Scholar 

  9. Ting, T.C.T.: Anisotropic Elasticity: Theory and Applications. Oxford University Press, New York (1996)

    Book  Google Scholar 

  10. England, A.H.: An arc crack around a circular elastic inclusion. ASME J. Appl. Mech. 33, 637–640 (1966)

    Article  ADS  Google Scholar 

  11. Perlman, A.B., Sih, G.C.: Elastostatic problems of curvilinear cracks in bonded dissimilar materials. Int. J. Eng. Sci. 5, 845–867 (1967)

    Article  Google Scholar 

  12. Toya, M.: A crack along the interface of a circular inclusion embedded in an infinite solid. J. Mech. Phys. Solids 22, 325–348 (1974)

    Article  ADS  Google Scholar 

  13. Herrmann, J.M.: The limitations of the model of a crack along the interface of an inclusion in an elastic matrix. Int. J. Solids Struct. 28, 1023–1039 (1991)

    Article  Google Scholar 

  14. Wang, X.: An isotropic circular inhomogeneity partially bonded to an anisotropic medium. Acta Mech. 227, 2947–2959 (2016)

    Article  MathSciNet  Google Scholar 

  15. Style, R.W., Wettlaufer, J.S., Dufresne, E.R.: Surface tension and the mechanics of liquid inclusions in compliant solids. Soft Matter 11(4), 672–679 (2015)

    Article  CAS  PubMed  ADS  Google Scholar 

  16. Style, R.W., Boltyanskiy, R., Allen, B., Jensen, K.E., Foote, H.P., Wettlaufer, J.S., Dufresne, E.R.: Stiffening solids with liquid inclusions. Nat. Phys. 11(1), 82–87 (2015)

    Article  CAS  Google Scholar 

  17. Wu, J., Ru, C.Q., Zhang, L.: An elliptical liquid inclusion in an infinite elastic plane. Proc. Royal Soc. A 474(2215), 201708 (2018)

    MathSciNet  Google Scholar 

  18. Chen, X., Li, M.X., Yang, M., Liu, S.B., Genin, G.M., Xu, F., Lu, T.J.: The elastic fields of a compressible liquid inclusion. Extreme Mechanics Letters 22, 122–130 (2018)

    Article  Google Scholar 

  19. Dai, M., Hua, J., Schiavone, P.: Compressible liquid/gas inclusion with high initial pressure in plane deformation: Modified boundary conditions and related analytical solutions. Euro. J. Mech. A-Solids 82, 104000 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  20. Dai, M., Schiavone, P.: Modified closed-form solutions for three-dimensional elastic deformations of a composite structure containing macro-scale spherical gas/liquid inclusions. Appl. Math. Modelling 97, 57–68 (2021)

    Article  MathSciNet  Google Scholar 

  21. Ti, F., Chen, X., Li, M.X., Sun, X.C., Liu, S.B., Lu, T.J.: Cylindrical compressible liquid inclusion with surface effects. J. Mech. Phys. Solids 161, 104813 (2022)

    Article  MathSciNet  CAS  Google Scholar 

  22. Ghosh, K., Lopez-Pamies, O.: Elastomers filled with liquid inclusions: theory, numerical implementation, and some basic results. J. Mech. Phys. Solids 166, 104930 (2022)

    Article  MathSciNet  Google Scholar 

  23. Ghosh, K., Lefevre, V., Lopez-Pamies, O.: The effective shear modulus of a random isotropic suspension of monodisperse liquid n-spheres: from the dilute limit to the percolation threshold. Soft Matter 19, 208–224 (2023)

    Article  CAS  PubMed  ADS  Google Scholar 

  24. Ghosh, K., Lefevre, V., Lopez-Pamies, O.: Homogenization of elastomers filled with liquid inclusions: The small-deformation limit. J. Elasticity 154, 235–253 (2023)

    Article  MathSciNet  Google Scholar 

  25. Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. P. Noordhoff Ltd., Groningen (1953)

    Google Scholar 

  26. Srolovitz, D.J., Luton, M.J., Petkovic-Luton, R., Barnett, D.M., Nix, W.D.: Diffusionally modified dislocation-particle elastic interactions. Acta Metall. 32, 1079–1088 (1984)

    Article  CAS  Google Scholar 

  27. Ekneligoda, T.C., Zimmerman, R.W.: Compressibility of two-dimensional pores having n-fold axes of symmetry. Proc. R. Soc. Lond. A 462, 1933–1947 (2006)

    MathSciNet  ADS  Google Scholar 

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Acknowledgements

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

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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, 10th Floor Donadeo Innovation Centre for Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Peter Schiavone

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  1. Xu Wang
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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Schiavone, P. A partially debonded circular elastic inhomogeneity with an incompressible liquid inclusion occupying the debonded section. Acta Mech 235, 897–906 (2024). https://doi.org/10.1007/s00707-023-03789-8

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  • DOI: https://doi.org/10.1007/s00707-023-03789-8

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