The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain

[+] Author and Article Information
M. Rahman

Daimler-Chrysler Corporation, CIMS 484-14-01, 800 Chrysler Drive, Auburn Hills, MI 48326-2757 e-mail: mr117@daimlerchrysler.com

J. Appl. Mech 69(5), 593-601 (Aug 16, 2002) (9 pages) doi:10.1115/1.1491270 History: Received June 05, 2001; Revised December 10, 2001; Online August 16, 2002
Copyright © 2002 by ASME
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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.
Eshelby,  J. D., 1959, “The Elastic Field Outside an Ellipsoidal Inclusion,” Proc. R. Soc. London, Ser. A, A252, pp. 561–569.
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.
Kinoshita,  N., and Mura,  T., 1971, “Elastic Fields of Inclusions in Anisotropic Media,” Phys. Status Solidi A, 5, pp. 759–768.
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.
Mura,  T., and Kinoshita,  N., 1978, “The Polynomial Eigenstrain Problem for an Anisotropic Ellipsoidal Inclusion,” Phys. Status Solidi A, 48, pp. 447–450.
Mura, T., 1987, Micromechanics of Defects in Solids, Martinus Nijhoff, The Hague.
Mura,  T., 1988, “Inclusion Problems,” Appl. Mech. Rev., 41(1), pp. 15–20.
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.
Markenscoff,  X., 1998, “Inclusions of Uniform Eigenstrains and Constant or Other Stress Dependence,” ASME J. Appl. Mech., 65, pp. 863–866.
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.
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.
Mikata,  Y., and Nemat-Nasser,  S., 1991, “Interaction of a Harmonic Wave With a Dynamically Transforming Inhomogeneity,” J. Appl. Phys., 70, pp. 2071–2078.
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.
Van Dyke,  M., 1974, “Analysis and Improvement of Perturbation Series,” Q. J. Mech. Appl. Math., XXVII, Pt. 4, pp. 423–450.
Bell, R. J. T., 1959, An Elementary Treatise on Coordinate Geometry of Three Dimensions, Macmillan, London.




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