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Original Articles

Analytic Formulation of Anti-Plane Elastic Field for an Elliptical Inhomogeneity with Polynomial Eigenstrains in Anisotropic Materials

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Pages 722-736 | Received 24 Sep 2011, Accepted 14 Feb 2012, Published online: 02 Jun 2014

References

  • N.J. Hardiman, Elliptic elastic inclusion in an infinite elastic plate, Q. J. Mech. Appl. Math., vol. 7, pp. 226–230, 1954.
  • J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc., vol. A241, pp. 376–396, 1957.
  • J.D. Eshelby, The elastic field outside an ellipsoidal inclusion, Proc. Roy. Soc., vol. A252, pp. 561–569, 1959.
  • J.D. Eshelby, Elastic inclusion and inhomogeneities. In: Progress in Solid Mechanics, Vol. 2, I.N. Sneddon and R. Hill, Eds., North Holland, Amsterdam, pp. 89–140, 1961.
  • D.J. Bacon, D.M. Barnett, and R.O. Scattergood, The anisotropic continuum theory of lattice defects, Prog. Mater. Sci., vol. 23, pp. 51–262, 1978.
  • J.R. Willis, Variational and related methods for the overall properties of composites, Adv. Appl. Mech., vol. 21, pp. 1–78, 1981.
  • T. Mura, Micromechanics of Defects in Solids, 2nd Ed., Martinus-Nijhoff, Dordrecht, Netherlands, 1987.
  • H.A Luo and G.J. Weng, On Eshelby's inclusion problem in a three-phase spherically concentric solid, and a modification of Mori-Tanaka's method, Mech. Mater., vol. 6, pp. 347–361, 1987.
  • T.C.T. Ting, Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York, 1996.
  • S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Solids, Elsevier, New York, 1999.
  • K. Markov and L. Preziosi, Heterogeneous Media: Micromechanics Modeling Methods and Simulations, Birkhauser Verlag, Switzerland, 2000.
  • V.A. Buryachenko, Multiparticle effective field and related methods in micromechanics of composite materials, Appl. Mech. Rev., vol. 54, pp. 1–47, 2001.
  • L.J. Walpole, The elastic field of an inclusion in an anisotropic medium, Proc. Roy. Soc. Lond., vol. A300, pp. 270–289, 1967.
  • N. Kinoshita and T. Mura, Elastic fields of inclusions in anisotropic media, Phys. Status Solidi A, vol. 5, pp. 759–768, 1971.
  • N. Kinoshita and T. Mura, An ellipsoidal inclusion with polynomial eigenstrains, Q. Appl. Math., vol. 44, no. 1, pp. 195–199, 1986.
  • T. Mura and N. Kinoshita, The polynomial eigenstrain problem for an anisotropic ellipsoidal inclusion, Phys. Status Solidi A, vol. 48, pp. 447–450, 1978.
  • M. Rahman, The isotropic ellipsoidal inclusion with a polynomial distribution of eigenstrain, ASME J. Appl. Mech., vol. 69, pp. 593–601, 2002.
  • G.P. Sendeckyj, Ellipsoidal inhomogeneity problem, Ph.D. Dissertation, Northwestern University, Evanston, IL, 1967.
  • Z.A. Moschovidis and T. Mura, Two-ellipsoidal inhomogeneities by the equivalent inclusion method, ASME J. Appl. Mech., vol. 42, pp. 847–852, 1975.
  • R.J. Asaro and D.M. Barnett, The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion, J. Mech. Phys. Solids, vol. 23, pp. 77–83, 1975.
  • H.M. Shodja and A.S. Sarvestani, Elastic fields in double inhomogeneity by the equivalent inclusion method, ASME J. Appl. Mech., vol. 68, pp. 3–10, 2001.
  • P. Sharma and R. Sharma, On the Eshelby's inclusion problem for ellipsoids with nonuniform dilatational Gaussian and exponential eigenstrains, ASME J. Appl. Mech., vol. 70, pp. 418–425, 2003.
  • J.R. Willis, Anisotropic elastic inclusion problems, Q. J. Mech. Appl. Math., vol. 17, pp. 157–174, 1964.
  • W.T. Chen, On the elliptic elastic inclusion in an anisotropic medium, Q. J. Mech. Appl. Math., vol. 20, pp. 307–313. 1967.
  • H.C. Yang and Y.T. Chou, Antiplane strain problems of an elliptic inclusion in an anisotropic medium, ASME J. Appl. Mech., vol. 44, pp. 437–441, 1977.
  • R.D. Bhargava and H.C. Radhakrishna, Elliptic inclusions in orthotropic media, J. Phys. Soc. Japan, vol. 19, pp. 396–405, 1964.
  • H.C. Yang and Y.T. Chou, Generalized plane problems of elastic inclusions in anisotropic solids, ASME J. Appl. Mech., vol. 43, pp. 424–430, 1976.
  • P.J. Withers, The determination of the elastic field of an ellipsoidal inclusion in a transversely isotropic medium, and its relevance to composite materials, Philos. Mag., vol. A59, pp. 759–781, 1989.
  • M. Rahman, Some problems of a rigid elliptical disk-inclusion bonded inside a transversely isotropic space: Part I & Part II, J. Appl. Mech., vol. 66, pp. 612–630, 1999.
  • H.Y. Yu, S.C. Sanday, and C.I. Chang, Elastic inclusion and inhomogeneities in transversely isotropic solids, Proc. Roy. Soc. Lond., vol. A444, pp. 239–252, 1994.
  • C.Q. Ru, Analytical solution for Eshelby's problem of an inclusion of arbitrary shape in a plane or half-plane, J. Appl. Mech., vol. 66, pp. 315–322, 1999.
  • G.H. Nie, L. Guo, C.K. Chan, and F.G. Shin, Non-uniform eigenstrain induced stress field in an elliptic inhomogeneity embedded in orthotropic media with complex roots, Int. J. Solids Struct., vol. 44, pp. 3575–3593, 2007.
  • G.H. Nie, L. Guo, C.K. Chan, and F.G. Shin, Non-uniform eigenstrain induced stress field in an elliptic inhomogeneity embedded in orthotropic media with purely imaginary roots, Mech. Adv. Mat. Struct., vol. 16, pp. 33–45, 2009.
  • L. Guo, G.H. Nie, and C.K. Chan, Elliptical inhomogeneity with polynomial eigenstrains embedded in orthotropic materials, Arch. Appl. Mech., vol. 81, pp. 157–170, 2011.
  • G.H. Nie, C.K. Chan, L. Luo, and F.G. Shin, Non-uniform eigenstrain induced anti-plane stress field in an elliptic inhomogeneity embedded in anisotropic media with a single plane of symmetry, Acta Mechanica, vol. 206, pp. 23–37, 2009.
  • N.I. Mushkelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen Publisher, 1953.

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