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TECHNICAL PAPERS

Effective Elastic Properties of Porous Materials With Randomly Dispersed Pores: Finite Deformation

[+] Author and Article Information
V. A. Levin

Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia

V. V. Lokhin

Institute of Mechanics, Moscow State University, Moscow 117234, Russia

K. M. Zingerman

Department of Applied Mathematics and Cybernetics, Tver State University, Tver 170000, Russia

J. Appl. Mech 67(4), 667-670 (Jan 03, 2000) (4 pages) doi:10.1115/1.1286287 History: Received September 09, 1998; Revised January 03, 2000
Copyright © 2000 by ASME
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References

Hashin,  Z., and Shtrikman,  S., 1963, “A Variational Approach to the Theory of the Elastic Behavior of Multiphase Materials,” J. Mech. Phys. Solids, 11, pp. 127–140.
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Willis,  J. R., 1991, “On Methods for Bounding the Overall Properties of Nonlinear Composites,” J. Mech. Phys. Solids, 39, No. 1, pp. 73–86.
Ponte Castaneda,  P., 1991, “The Effective Mechanical Properties of Nonlinear Isotropic Solids,” J. Mech. Phys. Solids, 39, No. 1, pp. 45–71.
Ponte Castaneda,  P., and Zaidman,  M., 1994, “Constitutive Models for Porous Materials With Evolving Microstructure,” J. Mech. Phys. Solids, 42, No. 9, pp. 1459–1497.
Horvay,  G., 1952, “The Plane-Stress Problem of Perforated Plates,” ASME J. Appl. Mech., 19, pp. 355–360.
Filshtinskiy,  L. A., 1964, “Stresses and Strains in Elastic Plane Weakened by Doubly Periodic System of Equal Circular Holes,” Prikl. Mat. Mekh., 28, pp. 430–441 (in Russian).
Abeyaratne,  R., and Triantafyllidis,  N., 1984, “An Investigation of Localization in Porous Elastic Material Using Homogenization Theory,” ASME J. Appl. Mech., 51, pp. 481–486.
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Kachanov,  M., Tsukrov,  I., and Shafiro,  B., 1994, “Effective Moduli of a Solid With Holes and Cavities of Various Shapes,” Appl. Mech. Rev., 47, No. 1, Part 2, pp. S151–S174.
Mauge,  C., and Kachanov,  M., 1994, “Effective Elastic Properties of an Anisotropic Material With Arbitrary Oriented Interacting Cracks,” J. Mech. Phys. Solids, 42, No. 4, pp. 561–584.
Shafiro,  B., and Kachanov,  M., 1997, “Materials With Fluid-Filled Pores of Various Shapes: Effective Elastic Properties and Fluid Pressure Polarization,” Int. J. Solids Struct., 34, No. 27, pp. 3517–3540.
Levin,  V. A., Lokhin,  V. V., and Zingerman,  K. M., 1996, “Method of Estimation of Effective Properties of Porous Bodies Undergoing Finite Deformation,” Int. J. Fract., 81, pp. R79–R82.
Levin, V. A., Lokhin, V. V., and Zingerman, K. M., 1997, “A Method of Estimation of Effective Characteristics of Porous Bodies Under Finite Deformations,” Mekh. Tver. Tela, No. 4, pp. 45–50 (in Russian).
Green, A. E., and Adkins, J. E., 1960, Large Elastic Deformations and Non-Linear Continuum Mechanics, Clarendon Press, Oxford, UK.
Lurie, A. I., 1990, Nonlinear Theory of Elasticity, North-Holland, Amsterdam.
Levin,  V. A., 1998, “Theory of Repeated Superposition of Large Deformations: Elastic and Viscoelastic Bodies,” Int. J. Solids Struct., 35, No. 20, pp. 2585–2600.
Levin,  V. A., and Zingerman,  K. M., 1998, “Interaction and Microfracturing Pattern for Succesive Origination (Introduction) of Pores in Elastic Bodies: Finite Deformation,” ASME J. Appl. Mech., 65, No. 2, pp. 431–435.
Mori,  T., and Tanaka,  K., 1973, “Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions,” Acta Metall., 21, pp. 571–574.
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Murnaghan, F. D., 1951, Finite Deformation of an Elastic Solids, John Wiley and Sons, New York.

Figures

Grahic Jump Location
Arrangement of nodes in the representative area; (a) N=2, (b) N=3
Grahic Jump Location
Effective linear elastic moduli λe,Ge and upper Hashin-Shtrikman bounds λh,Gh referred to the correspondent matrix moduli versus porosity
Grahic Jump Location
Coefficients a3,a5,a6 versus porosity
Grahic Jump Location
Coefficients b33,b55,b46 versus porosity
Grahic Jump Location
Coefficients b34,b54,b35 versus porosity
Grahic Jump Location
Coefficients b53,b63,b65 versus porosity
Grahic Jump Location
Effect of the computational parameters on the plot of the coefficient a6 versus porosity

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