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TECHNICAL PAPERS

Asymptotic Solutions of Penny-Shaped Inhomogeneities in Global Eshelby’s Tensor

[+] Author and Article Information
Q. Yang, W. Y. Zhou

Department of Hydraulic Engineering, Tsinghua University, 100084 Beijing, P. R. China

G. Swoboda

Faculty of Civil Engineering and Architecture, University of Innsbruck, Technikerstr. 13 A-6020 Innsbruck, Austriae-mail: gunter.swoboda@uibk.ac.at

J. Appl. Mech 68(5), 740-750 (Jan 08, 2001) (11 pages) doi:10.1115/1.1380676 History: Received April 18, 2000; Revised January 08, 2001
Copyright © 2001 by ASME
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References

Mura, T., 1987, Micromechanics of Defects in Solids, 2nd Ed., Martinus Nijhoff, Dordrecht, The Netherlands.
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.
Hurtado,  J. A., Dundurs,  J., and Mura,  T., 1996, “Lamellar Inhomogeneities in a Uniform Stress Field,” J. Mech. Phys. Solids, 44, pp. 1–21.
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Zhao,  Y. H., and Weng,  G. J., 1996, “Plasticity of a Two-Phase Composite With Partially Debonded Inclusions,” Int. J. Plast., 12, pp. 781–804.
Shafiro,  B., and Kachanov,  M., 1999, “Solids With Non-Spherical Cavities: Simplified Representations of Cavity Compliance Tensors and the Overall Anisotropy,” J. Mech. Phys. Solids, 47, pp. 877–898.
Kachanov,  M., 1980, “A Continuum Model of Medium With Cracks,” J. Eng. Mech., 106, pp. 1039–1051.
Swoboda,  G., and Yang,  Q., 1999, “An Energy-Based Damage Model of Geomaterials—I. Formulation and Numerical Results,” Int. J. Solids Struct., 36, pp. 1719–1734.
Swoboda,  G., and Yang,  Q., 1999, “An Energy-Based Damage Model of Geomaterials—II. Deduction of Damage Evolution Laws,” Int. J. Solids Struct., 36, pp. 1735–1755.
Yang,  Q., Zhou,  W. Y., and Swoboda,  G., 1999, “Micromechanical Identification of Anisotropic Damage Evolution Laws,” Int. J. Fract., 98, pp. 55–76.
Budiansky,  B., and O’Connell,  R. J., 1976, “Elastic Moduli of a Cracked Solid,” Int. J. Solids Struct., 12, pp. 81–97.
Yang, Q., 1996, “Numerical Modeling for Discontinuous Geomaterials Considering Damage Propagation and Seepage,” Ph.D. thesis, Faculty of Architecture and Civil Engineering, University of Innsbruck, Austria.
Hurtado,  J. A., 1997, “Estudio de fibras de forma laminar en un campo de tensión uniforme: Grietas, anti-grietas y cuasi-grietas,” Anales de Mecánica de la Fractura, 14, pp. 105–110.
Gurson,  A. L., 1977, “Continuum Theory of Ductile Rupture by Void Nucleation and Growth, I. Yield Criteria and Flow Rules for Porous Ductile Media,” ASME J. Eng. Mater. Technol., 99, pp. 2–15.

Figures

Grahic Jump Location
(a) Inclusion or inhomogeneity Ω; (b) an ellipsoidal inclusion with principal half-axes a1,a2, and a3
Grahic Jump Location
Global and local coordinate system
Grahic Jump Location
(a) The Eshelby’s equivalent inclusion Ω of the penny-shaped inhomogeneity; (b) the energy-based equivalent inclusion Ωeq of the same inhomogeneity
Grahic Jump Location
(a) The Eshelby’s equivalent inclusion of a crack; (b) the spherical energy-based equivalent inclusion of the same crack
Grahic Jump Location
The variation of h with respect to α and ν0
Grahic Jump Location
The evolution of the energy-based equivalent inclusion Ωeq during the damaging process of a penny-shaped inhomogeneity: stiffness degrading, debonding, and cracking

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