A method is developed for derivation of effective constitutive equations for porous nonlinear-elastic materials undergoing finite strains. It is shown that the effective constitutive equations that are derived using the proposed approach do not change if a rigid motion is superimposed on the deformation. An approach is proposed for the computation of effective characteristics for nonlinear-elastic materials in which pores are originated after a preliminary loading. This approach is based on the theory of superimposed finite deformations. The results of computations are presented for plane strain, when pores are distributed uniformly.
Issue Section:
Technical Papers
1.
Hashin
, Z.
, and Rozen
, B. W.
, 1964
, “The Elastic Moduli of Fiber Reinforced Materials
,” ASME J. Appl. Mech.
, 31
, pp. 223
–232
.2.
Christensen, R. M., 1979, Mechanics of Composite Materials, John Wiley and Sons, New York.
3.
Kachanov
, M.
, Tsukrov
, I.
, and Shafiro
, B.
, 1994
, “Effective Moduli of a Solid With Holes and Cavities of Various Shapes
,” Appl. Mech. Rev.
, 47
, pp. S151–S174
S151–S174
.4.
Mauge
, C.
, and Kachanov
, M.
, 1994
, “Effective Elastic Properties of an Anisotropic Material With Arbitrary Oriented Interacting Cracks
,” J. Mech. Phys. Solids
, 42
, pp. 561
–584
.5.
Zhikov, V. V., Kozlov, S. M., and Olejnik, O. A., 1994, Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin.
6.
Braides
, A.
, 1985
, “Homogenization of some almost periodic functional
,” Rendiconti. Accademia Nazionale delle Scienze
, XL
(103
), pp. 313
–322
.7.
Mu¨ller
, S.
, 1987
, “Homogenization of Nonconvex Integral Functionals and Cellular Elastic Material
,” Arch. Ration. Mech. Anal.
, 99
, pp. 189
–212
.8.
Braides
, A.
, Defranceschi
, A.
, and Vitali
, E.
, 1996
, “Homogenization of Free Discontinuity Problems
,” Arch. Ration. Mech. Anal.
, 135
(4
), pp. 297
–356
.9.
Vavakin
, A. S.
, and Salganik
, R. L.
, 1975
, “Effective Characteristics of Nonhomogeneous Media With Isolated Inhomogeneities
,” Izvestia AN SSSR, Mekhanika Tverdogo Tela
, (3
), pp. 65
–75
(in Russian).10.
Lurie, A. I., 1990, Nonlinear Theory of Elasticity, North-Holland, Amsterdam.
11.
Brovko
, G. L.
, and Ilyushin
, A. A.
, 1993
, “On a Plane Model of Perforated Plates
,” Moscow Univ. Mech. Bull.
, (2
), pp. 83
–91
.12.
Hill
, R.
, 1972
, “On Constitutive Macrovariables for Heterogeneous Solids at Finite Strain
,” Proc. R. Soc. London, Ser. A
, 326
(1565
), pp. 131
–147
.13.
Levin
, V. A.
, Lokhin
, V. V.
, and Zingerman
, K. M.
, 1997
, “A Method of Estimation of Effective Characteristics of Porous Bodies Under Finite Deformations
,” Mekhanika Tverdogo Tela
, (4
), pp. 45
–50
(in Russian).14.
Levin
, V. A.
, Lokhin
, V. V.
, and Zingerman
, K. M.
, 2000
, “Effective Elastic Properties of Porous Materials With Randomly Dispersed Pores: Finite Deformation
,” ASME J. Appl. Mech.
, 67
, pp. 667
–670
.15.
Levin
, V. A.
, and Zingerman
, K. M.
, “The Influence of Small Defects on the Stress Concentration Near a Hole
,” Phys. Dokl.
, 47
(10
), pp. 738
–741
.16.
Zhurkov
, S. N.
, and Kuksenko
, V. S.
, 1975
, “The Micromechanics of Polymer Fracture
,” Int. J. Fract.
, 11
, pp. 629
–639
.17.
Zhurkov, S. N., Kuksenko, V. S., and Slutsker, A. I., 1969, “Submicrocrack Formation Under Stress,” Proc. Second International Conference on Fracture, Chapman and Hall, London, pp. 531–549.
18.
Tamuzh, V. P., and Kuksenko, V. S., 1978, Micromechanics of Fracture of Polymeric Materials, Zinatne, Riga (in Russian).
19.
Levin
, V. A.
, 1998
, “Theory of Repeated Superposition of Large Deformations. Elastic and Viscoelastic Bodies
,” Int. J. Solids Struct.
, 35
, pp. 2585
–2600
.20.
Levin, V. A., 1999, Repeated Superposition of Large Deformations in Elastic and Viscoelastic Solids, Nauka (Science), Moscow (in Russian).
21.
Gent
, A. N.
, 1990
, “Cavitation in Rubber: A Cautionary Tale
,” Rubber Chem. Technol.
, 63
, pp. G49–G53
G49–G53
.22.
Horgan
, C. O.
, and Poligone
, D. A.
, 1995
, “Cavitation in Nonlinearly Elastic Solids: A Review
” Appl. Mech. Rev.
, 48
, pp. 471
–485
.23.
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
, pp. 431
–435
.24.
Murnaghan, F. D., 1951, Finite Deformation of an Elastic Solid, John Wiley and Sons, New York.
25.
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
.26.
Guz
, A. N.
, Makhort
, F. G.
, Gushcha
, O. I.
, and Lebedev
, V. K.
, 1970
, “On the Theory of Wave Distribution in Elastic Isotropic Medium Subjected to Initial Strains
,” Prikl. Mekh.
, 6
(12
), pp. 42
–49
.27.
Zubov
, L. M.
, and Rudev
, A. N.
, 1992
, “The Effective Method for the Verification of Hadamard’s Condition in a Nonlinear Elastic Compressible Medium
,” Prikl. Mat. Mekh.
, 56
(2
), pp. 296
–305
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