In this paper, a three-dimensional penny-shaped isotropic inhomogeneity surrounded by unbounded isotropic matrix in a uniform stress field is studied based on Eshelby’s equivalent inclusion method. The solution including the deduced equivalent eigenstrain and its asymptotic expressions is presented in tensorial form. The so-called energy-based equivalent inclusion method is introduced to remove the singularities of the size and eigenstrain of the Eshelby’s equivalent inclusion of the penny-shaped inhomogeneity, and yield the same energy disturbance. The size of the energy-based equivalent inclusion can be used as a generic damage measurement.
Issue Section:
Technical Papers
1.
Mura, T., 1987, Micromechanics of Defects in Solids, 2nd Ed., Martinus Nijhoff, Dordrecht, The Netherlands.
2.
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
.3.
Hurtado
, J. A.
, Dundurs
, J.
, and Mura
, T.
, 1996
, “Lamellar Inhomogeneities in a Uniform Stress Field
,” J. Mech. Phys. Solids
, 44
, pp. 1
–21
.4.
Homentcovschi
, D.
, and Dascalu
, C.
, 1996
, “Uniform Asymptotic Solutions for Lamellar Inhomogeneities in Plane Elasticity
,” J. Mech. Phys. Solids
, 44
, pp. 1
–21
.5.
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
.6.
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
.7.
Kachanov
, M.
, 1980
, “A Continuum Model of Medium With Cracks
,” J. Eng. Mech.
, 106
, pp. 1039
–1051
.8.
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
.9.
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
.10.
Yang
, Q.
, Zhou
, W. Y.
, and Swoboda
, G.
, 1999
, “Micromechanical Identification of Anisotropic Damage Evolution Laws
,” Int. J. Fract.
, 98
, pp. 55
–76
.11.
Budiansky
, B.
, and O’Connell
, R. J.
, 1976
, “Elastic Moduli of a Cracked Solid
,” Int. J. Solids Struct.
, 12
, pp. 81
–97
.12.
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.
13.
Hurtado
, J. A.
, 1997
, “Estudio de fibras de forma laminar en un campo de tensio´n uniforme: Grietas, anti-grietas y cuasi-grietas
,” Anales de Meca´nica de la Fractura
, 14
, pp. 105
–110
.14.
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
.Copyright © 2001
by ASME
You do not currently have access to this content.