DOI: 10.1115/1.1491270. The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain

The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain

10.1115/1.1491270

Crossref journal-article

ASME International

Journal of Applied Mechanics (33)

Abstract

We consider the problem of determining the elastic field in an infinite elastic solid induced by an ellipsoidal inclusion with a distribution of eigenstrains. The particular type of distribution considered in the article is characterized by a polynomial in the Cartesian coordinates of the points of the inclusion. Eshelby showed that in such a situation the induced strain field within the inclusion is also characterized by a polynomial of the same order. However, the explicit expression for this polynomial seems to have not yet been reported in the literature. The present study fills this gap.

Bibliography

Rahman, M. (2002). The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain. Journal of Applied Mechanics, 69(5), 593â601.

Authors 1

M. Rahman (first)

References 25 Referenced 51

Eshelby, J. D. , 1957, “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,” Proc. R. Soc. London, Ser. A, A241, pp. 376–396. (10.1098/rspa.1957.0133)
Eshelby, J. D. , 1959, “The Elastic Field Outside an Ellipsoidal Inclusion,” Proc. R. Soc. London, Ser. A, A252, pp. 561–569. (10.1098/rspa.1959.0173)
Eshelby, J. D., 1960, “Elastic Inclusions and Inhomogeneities,” Progress in Solid Mechanics, 2, I. N. Sneddon and R. Hill, eds., North-Holland, Amsterdam, pp. 89–140.
Walpole, L. J. , 1967, “The Elastic Field of an Inclusion in an Anisotropic Medium,” Proc. R. Soc. London, Ser. A, 300, pp. 270–289. (10.1098/rspa.1967.0170)
Kinoshita, N., and Mura, T., 1971, “Elastic Fields of Inclusions in Anisotropic Media,” Phys. Status Solidi A, 5, pp. 759–768. (10.1002/pssa.2210050332)
Kinoshita, N., and Mura, T., 1986, “An Ellipsoidal Inclusion With Polynomial Eigenstrains,” Q. Appl. Math., XLIV(1), pp. 195–199.
Asaro, R. J., and Barnett, D. M., 1975, “The Non-uniform Transformation Strain Problem for an Anisotropic Ellipsoidal Inclusion,” J. Mech. Phys. Solids, 23, pp. 77–83. (10.1016/0022-5096(75)90012-5)
Mura, T., and Kinoshita, N., 1978, “The Polynomial Eigenstrain Problem for an Anisotropic Ellipsoidal Inclusion,” Phys. Status Solidi A, 48, pp. 447–450. (10.1002/pssa.2210480222)
Mura, T., 1987, Micromechanics of Defects in Solids, Martinus Nijhoff, The Hague. (10.1007/978-94-009-3489-4)
Mura, T. , 1988, “Inclusion Problems,” Appl. Mech. Rev., 41(1), pp. 15–20. (10.1115/1.3151875)
Nemat-Nasser, S., and Hori, M., 1999, Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Amsterdam.
Khachaturyan, A. G., 1983, Theory of Structural Transformations in Solids, John Wiley and Sons, New York.
Markenscoff, X. , 1998, “On the Shape of the Eshelby Inclusions,” J. Elast., 44, pp. 163–166.
Markenscoff, X. , 1998, “Inclusions With Constant Eigenstress,” J. Mech. Phys. Solids, 46, pp. 2297–2301. (10.1016/S0022-5096(98)00039-8)
Markenscoff, X. , 1998, “Inclusions of Uniform Eigenstrains and Constant or Other Stress Dependence,” ASME J. Appl. Mech., 65, pp. 863–866. (10.1115/1.2791923)
Lubarda, V. A., and Markenscoff, X., 1998, “On the Absence of Eshelby Property for Non-ellipsoidal Inclusions,” Int. J. Solids Struct., 35, No. 25, pp. 3405–3411. (10.1016/S0020-7683(98)00025-0)
Ferrers, N. M. , 1877, “On the Potentials of Ellipsoids, Ellipsoidal Shells, Elliptic Laminae and Elliptic Rings of Variable Densities,” Q. J. Pure Appl. Math., 14(1), pp. 1–22.
Dyson, F. D. , 1891, “The Potentials of Ellipsoids of Variable Densities,” Q. J. Pure Appl. Math., XXV, pp. 259–288.
Rahman, M. , 2001, “On the Newtonian Potentials of Heterogeneous Ellipsoids and Elliptic Discs,” Proc. R. Soc. London, Ser. A, A457(2013), pp. 2227–2250.
Natanson, I. P., 1967, Theory of Functions of a Real Variable, Frederick Ungar, New York.
Mikata, Y., and Nemat-Nasser, S., 1990, “Elastic Field due to a Dynamically Transforming Spherical Inclusion,” ASME J. Appl. Mech., 57, pp. 845–849. (10.1115/1.2897650)
Mikata, Y., and Nemat-Nasser, S., 1991, “Interaction of a Harmonic Wave With a Dynamically Transforming Inhomogeneity,” J. Appl. Phys., 70, pp. 2071–2078. (10.1063/1.349442)
Cheng, Z.-Q., and Batra, R. C., 1999, “Exact Eshelby Tensor for a Dynamic Circular Cylindrical Inclusion,” ASME J. Appl. Mech., 66, pp. 563–565. (10.1115/1.2791087)
Van Dyke, M. , 1974, “Analysis and Improvement of Perturbation Series,” Q. J. Mech. Appl. Math., XXVII, Pt. 4, pp. 423–450. (10.1093/qjmam/27.4.423)
Bell, R. J. T., 1959, An Elementary Treatise on Coordinate Geometry of Three Dimensions, Macmillan, London.

Dates

Type	When
Created	22 years, 11 months ago (Oct. 1, 2002, 11:31 a.m.)
Deposited	5 years, 10 months ago (Oct. 4, 2019, 12:32 p.m.)
Indexed	1 week, 3 days ago (Aug. 23, 2025, 9:13 p.m.)
Issued	23 years ago (Aug. 16, 2002)
Published	23 years ago (Aug. 16, 2002)
Published Online	23 years ago (Aug. 16, 2002)
Published Print	23 years ago (Sept. 1, 2002)

Funders 0

None

BibTeX

@article{Rahman_2002, title={The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain}, volume={69}, ISSN={1528-9036}, url={http://dx.doi.org/10.1115/1.1491270}, DOI={10.1115/1.1491270}, number={5}, journal={Journal of Applied Mechanics}, publisher={ASME International}, author={Rahman, M.}, year={2002}, month=aug, pages={593–601} }

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