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Volumn 45, Issue 4, 1997, Pages 611-636

Tangential stiffness of elastic materials with systems of growing or closing cracks

Author keywords

A. Microcracking; B. Concrete; B. Constitutive behaviour; B. Crack mechanics; C. Rock

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONCRETES; CRACK PROPAGATION; ENERGY DISSIPATION; FRACTURE MECHANICS; ITERATIVE METHODS; POLYNOMIALS; STIFFNESS; STRAIN; STRESSES; TENSORS;

EID: 0031117914     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(96)00127-5     Document Type: Article
Times cited : (44)

References (52)
  • 1
    • 0028166630 scopus 로고
    • Nonlocal damage theory based on micromechanics of crack interactions
    • Addendum and Errata, 1401-1402
    • Bažant, Z. P. (1994) Nonlocal damage theory based on micromechanics of crack interactions. ASCE J. Engng Mech. 120, 593-617; Addendum and Errata, 1401-1402.
    • (1994) ASCE J. Engng Mech. , vol.120 , pp. 593-617
    • Bažant, Z.P.1
  • 2
    • 3242763203 scopus 로고
    • Damage nonlocality due to microcrack interactions: Statistical determination of crack influence function
    • ed. Z. P. Bažant, Z. Bittnar, M. Jirásek and J. Mazars, E & FN SPON, London
    • Bažant, Z. P. and Jirásek, M. (1994) Damage nonlocality due to microcrack interactions: statistical determination of crack influence function. In Fracture and Damage in Quasi-Brittle Structures, ed. Z. P. Bažant, Z. Bittnar, M. Jirásek and J. Mazars, pp. 3-17. E & FN SPON, London.
    • (1994) Fracture and Damage in Quasi-brittle Structures , pp. 3-17
    • Bažant, Z.P.1    Jirásek, M.2
  • 3
    • 0022046380 scopus 로고
    • Microplane model for progressive fracture of concrete and rock
    • Bažant, Z. P. and Oh, B. H. (1985) Microplane model for progressive fracture of concrete and rock. ASCE J. Engng Mech. 111, 559-582.
    • (1985) ASCE J. Engng Mech. , vol.111 , pp. 559-582
    • Bažant, Z.P.1    Oh, B.H.2
  • 4
    • 0022593796 scopus 로고
    • Efficient numerical integration on the surface of a sphere
    • Bažant, Z. P. and Oh, B.-H. (1986) Efficient numerical integration on the surface of a sphere. Z. angew. Math. u. Mech. (ZAMM) 66, 37-49.
    • (1986) Z. Angew. Math. U. Mech. (ZAMM) , vol.66 , pp. 37-49
    • Bažant, Z.P.1    Oh, B.-H.2
  • 5
    • 0024101709 scopus 로고
    • Microplane model for brittle-plastic material: I. Theory
    • Bažant, Z. P. and Prat, P. C. (1988a) Microplane model for brittle-plastic material: I. Theory. ASCE J. Engng Mech. 114, 1672-1688.
    • (1988) ASCE J. Engng Mech. , vol.114 , pp. 1672-1688
    • Bažant, Z.P.1    Prat, P.C.2
  • 6
    • 0024101650 scopus 로고
    • Microplane model for brittle-plastic material: II. Verification
    • Bažant, Z. P. and Prat,. P. C. (1988b) Microplane model for brittle-plastic material: II. Verification. ASCE J. Engng Mech. 114, 1689-1702.
    • (1988) ASCE J. Engng Mech. , vol.114 , pp. 1689-1702
    • Bažant, Z.P.1    Prat, P.C.2
  • 7
    • 30244528592 scopus 로고
    • Elastic material with growing or closing cracks: Tangential stiffness
    • S. N. Atluri, ed. R. Batra, Society of Engineering Science, 32nd Annual Meeting, Springer Verlag
    • Bažant, Z. P. and Prat, P. C. (1995) Elastic material with growing or closing cracks: tangential stiffness. In Contemporary Research in Engineering Science, Proceedings, Eringen Medal Symposium honoring S. N. Atluri, ed. R. Batra, pp. 55-65. Society of Engineering Science, 32nd Annual Meeting, Springer Verlag.
    • (1995) Contemporary Research in Engineering Science, Proceedings, Eringen Medal Symposium Honoring , pp. 55-65
    • Bažant, Z.P.1    Prat, P.C.2
  • 8
    • 0001144972 scopus 로고    scopus 로고
    • Microplane for concrete: I. Stress-strain boundaries and finite strain
    • Bažant, Z. P., Xiang, Y. and Prat, P. C. (1996a) Microplane for concrete: I. Stress-strain boundaries and finite strain. ASCE J. Engng Mech. 122, 245-262.
    • (1996) ASCE J. Engng Mech. , vol.122 , pp. 245-262
    • Bažant, Z.P.1    Xiang, Y.2    Prat, P.C.3
  • 9
  • 10
    • 8344236638 scopus 로고
    • On the elastic moduli of some heterogeneous materials
    • Budiansky, B. (1965) On the elastic moduli of some heterogeneous materials. J. Mech. Phys. Solids 13, 223-227.
    • (1965) J. Mech. Phys. Solids , vol.13 , pp. 223-227
    • Budiansky, B.1
  • 12
    • 0038210695 scopus 로고
    • Smeared analysis of concrete fracture using a microplane based multicrack model with static constraint
    • ed. J. G. M. van Mier, J. G. Rots and A. Bakker, E & FN SPON, London
    • Carol, I. and Prat, P. C. (1991) Smeared analysis of concrete fracture using a microplane based multicrack model with static constraint. In Fracture Processes in Concrete, Rock and Ceramics, ed. J. G. M. van Mier, J. G. Rots and A. Bakker, pp. 619-628. E & FN SPON, London.
    • (1991) Fracture Processes in Concrete, Rock and Ceramics , pp. 619-628
    • Carol, I.1    Prat, P.C.2
  • 13
    • 0004166768 scopus 로고
    • A multicrack model based on the theory of multisurface plasticity and two fracture energies
    • ed. D. R. J. Owen, E. Oñate and E. Hinton, Pineridge Press, Barcelona
    • Carol, I. and Prat, P. C. (1995) A multicrack model based on the theory of multisurface plasticity and two fracture energies. In Computational Plasticity (COMPLAS IV), ed. D. R. J. Owen, E. Oñate and E. Hinton, Vol. 2, pp. 1583-1594. Pineridge Press, Barcelona.
    • (1995) Computational Plasticity (COMPLAS IV) , vol.2 , pp. 1583-1594
    • Carol, I.1    Prat, P.C.2
  • 14
    • 3843083995 scopus 로고
    • Numerical analysis of mixed-mode fracture of quasibrittle materials using a multicrack constitutive model
    • ed. H. P. Rossmanith and K. J. Miller, Mechanical Engineering Publications Ltd., London
    • Carol, I., Prat, P. C. and Gettu, R. (1993) Numerical analysis of mixed-mode fracture of quasibrittle materials using a multicrack constitutive model. In Mixed-Mode Fatigue and Fracture, ed. H. P. Rossmanith and K. J. Miller, pp. 319-332. Mechanical Engineering Publications Ltd., London.
    • (1993) Mixed-mode Fatigue and Fracture , pp. 319-332
    • Carol, I.1    Prat, P.C.2    Gettu, R.3
  • 16
    • 0018506068 scopus 로고
    • Solutions for effective shear properties in hree-phase sphere and cylinder models
    • Christensen, R. M. and Lo, K. H. (1979) Solutions for effective shear properties in hree-phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315-330.
    • (1979) J. Mech. Phys. Solids , vol.27 , pp. 315-330
    • Christensen, R.M.1    Lo, K.H.2
  • 17
    • 0000913283 scopus 로고
    • Transformation field analysis of inelastic composite materials
    • Dvorak, G. J. (1992) Transformation field analysis of inelastic composite materials. Proc. Rov. Soc. London A437, 311-327.
    • (1992) Proc. Rov. Soc. London , vol.A437 , pp. 311-327
    • Dvorak, G.J.1
  • 18
    • 0000913283 scopus 로고
    • Transformation field analysis of inelastic composite materials
    • Dvorak, G. J. and Benveniste, Y. (1992) Transformation field analysis of inelastic composite materials. Proc. Roy. Soc. London A437, 291-310.
    • (1992) Proc. Roy. Soc. London , vol.A437 , pp. 291-310
    • Dvorak, G.J.1    Benveniste, Y.2
  • 19
    • 0000929676 scopus 로고
    • The determination of the elastic field of an ellipsoidal inclusion, and related problems
    • Eshelby, J. D. (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. London A241, 376-396.
    • (1957) Proc. Roy. Soc. London , vol.A241 , pp. 376-396
    • Eshelby, J.D.1
  • 20
    • 0023349506 scopus 로고
    • Close interaction of coplanar circular cracks in an elastic medium
    • Fabrikant, U. I. (1987) Close interaction of coplanar circular cracks in an elastic medium. Acta Mech. 67, 39-59.
    • (1987) Acta Mech. , vol.67 , pp. 39-59
    • Fabrikant, U.I.1
  • 21
    • 0027622140 scopus 로고
    • Effective stiffness of a periodically cracked 3-D solid
    • Fares, N. (1993) Effective stiffness of a periodically cracked 3-D solid. Int. J. Fracture 62, 149-162.
    • (1993) Int. J. Fracture , vol.62 , pp. 149-162
    • Fares, N.1
  • 22
    • 0001623598 scopus 로고
    • The differential scheme and its application to cracked materials
    • Hashin, Z. (1988) The differential scheme and its application to cracked materials. J. Mech. Phys. Solids 36, 719-734.
    • (1988) J. Mech. Phys. Solids , vol.36 , pp. 719-734
    • Hashin, Z.1
  • 23
    • 85143526052 scopus 로고
    • The elasticity of an anisotropic aggregate of anisotropic cubic crystals
    • Hershey, A. V. and Dahlgren, V. A. (1954) The elasticity of an anisotropic aggregate of anisotropic cubic crystals. J. Appl. Mech. 21, 236-241.
    • (1954) J. Appl. Mech. , vol.21 , pp. 236-241
    • Hershey, A.V.1    Dahlgren, V.A.2
  • 24
    • 11644304284 scopus 로고
    • A self-consistent mechanics of composite materials
    • Hill, R. (1965) A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213-222.
    • (1965) J. Mech. Phys. Solids , vol.13 , pp. 213-222
    • Hill, R.1
  • 25
    • 0018061810 scopus 로고
    • The behavior of a flat elliptical crack in an anisotropic elastic body
    • Hoenig, A. (1978) The behavior of a flat elliptical crack in an anisotropic elastic body. Int. J. Solids and Structures 14, 925-934.
    • (1978) Int. J. Solids and Structures , vol.14 , pp. 925-934
    • Hoenig, A.1
  • 26
    • 0018286558 scopus 로고
    • Elastic moduli of a non-randomly cracked body
    • Hoenig, A. (1979) Elastic moduli of a non-randomly cracked body. Int. J. Solids Structures 15, 137-154.
    • (1979) Int. J. Solids Structures , vol.15 , pp. 137-154
    • Hoenig, A.1
  • 27
    • 0020499204 scopus 로고
    • Overall moduli of solids with microcracks: Load-induced anisotropy
    • Horii, H. and Nemat-Nasser, S. (1983) Overall moduli of solids with microcracks: load-induced anisotropy. J. Mech. Phys. Solids 31, 155-171.
    • (1983) J. Mech. Phys. Solids , vol.31 , pp. 155-171
    • Horii, H.1    Nemat-Nasser, S.2
  • 28
    • 0021897717 scopus 로고
    • Elastic fields of interacting inhomogeneities
    • Horii, H. and Nemat-Nasser, S. (1985) Elastic fields of interacting inhomogeneities. Int. J. Solids Structures 21, 731-745.
    • (1985) Int. J. Solids Structures , vol.21 , pp. 731-745
    • Horii, H.1    Nemat-Nasser, S.2
  • 29
    • 0027642866 scopus 로고
    • Estimation of the elastic properties of fractured rock masses
    • Hu, K. X. and Huang, Y. (1993) Estimation of the elastic properties of fractured rock masses. Int. J. Rock Mech. Min. Sci. 30, 381-394.
    • (1993) Int. J. Rock Mech. Min. Sci. , vol.30 , pp. 381-394
    • Hu, K.X.1    Huang, Y.2
  • 30
    • 0028574501 scopus 로고
    • A self-consistent mechanics method for solids containing inclusions and a general distribution of cracks
    • Huang, Y., Hu, K. X. and Chandra, A. (1994) A self-consistent mechanics method for solids containing inclusions and a general distribution of cracks. Acta Mech. 105, 69-84.
    • (1994) Acta Mech. , vol.105 , pp. 69-84
    • Huang, Y.1    Hu, K.X.2    Chandra, A.3
  • 31
    • 0028465793 scopus 로고
    • Localization analysis of nonlocal model based on crack interactions
    • Jirásek, M. and Bažant, Z. P. (1994) Localization analysis of nonlocal model based on crack interactions. ASCE J. Engng Mech. 120, 1521-1542.
    • (1994) ASCE J. Engng Mech. , vol.120 , pp. 1521-1542
    • Jirásek, M.1    Bažant, Z.P.2
  • 32
    • 0028443540 scopus 로고
    • Effective elastic moduli of two-dimensional brittle solids with interacting microcracks. Part I: Basic formulations. Part II: Evolutionary damage models
    • Ju, J. W. and Chen, T.-M. (1994) Effective elastic moduli of two-dimensional brittle solids with interacting microcracks. Part I: Basic formulations. Part II: Evolutionary damage models. J. Appl. Mech. 61, 349-366.
    • (1994) J. Appl. Mech. , vol.61 , pp. 349-366
    • Ju, J.W.1    Chen, T.-M.2
  • 33
    • 0000431818 scopus 로고
    • A three-dimensional statistical micromechanical theory for brittle solids with interacting microcracks
    • Ju, J. W. and Tseng, K. H. (1992) A three-dimensional statistical micromechanical theory for brittle solids with interacting microcracks. Int. J. Damage Mech. 1, 102-131.
    • (1992) Int. J. Damage Mech. , vol.1 , pp. 102-131
    • Ju, J.W.1    Tseng, K.H.2
  • 34
    • 0000477742 scopus 로고
    • Continuum model of medium with cracks
    • Kachanov, M. (1980) Continuum model of medium with cracks. ASCE J. Engng Mech. Div. 106(EM5), 1039-1051.
    • (1980) ASCE J. Engng Mech. Div. , vol.106 , Issue.EM5 , pp. 1039-1051
    • Kachanov, M.1
  • 35
    • 0023164009 scopus 로고
    • Elastic solids with many cracks: A simple method of analysis
    • Kachanov, M. (1987a) Elastic solids with many cracks: a simple method of analysis. Int. J. Solids Structures 23, 23-43.
    • (1987) Int. J. Solids Structures , vol.23 , pp. 23-43
    • Kachanov, M.1
  • 36
    • 0023535667 scopus 로고
    • On modelling of anisotropic damage in elastic-brittle materials - A brief review
    • ed. A. Wang and G. Haritos, ASME Winter, Annual Meeting, ASME, Boston
    • Kachanov, M. (1987b) On modelling of anisotropic damage in elastic-brittle materials - a brief review. In Damage Mechanics oj Composites, ed. A. Wang and G. Haritos, ASME Winter, Annual Meeting, pp. 99-105. ASME, Boston.
    • (1987) Damage Mechanics OJ Composites , pp. 99-105
    • Kachanov, M.1
  • 37
    • 84922325988 scopus 로고
    • Effective elastic properties of cracked solids : Critical review of some basic concepts
    • Kachanov, M. (1992) Effective elastic properties of cracked solids : critical review of some basic concepts. Appl. Mech. Rev. 45, 304-335.
    • (1992) Appl. Mech. Rev. , vol.45 , pp. 304-335
    • Kachanov, M.1
  • 38
    • 49549088687 scopus 로고
    • Elastic solids with many cracks and related problems
    • ed. J. Hutchinson and T. Wu, Academic Press
    • Kachanov, M. (1993) Elastic solids with many cracks and related problems. In Advances in Applied Mechanics, ed. J. Hutchinson and T. Wu, Vol. 30, pp. 259-445. Academic Press.
    • (1993) Advances in Applied Mechanics , vol.30 , pp. 259-445
    • Kachanov, M.1
  • 39
    • 84973797549 scopus 로고
    • Effective moduli of solids with cavities of various shapes
    • Kachanov, M., Tsukrov, I. and Shafiro, B. (1994) Effective moduli of solids with cavities of various shapes. Appl. Mech. Rev. 47, S151-S174.
    • (1994) Appl. Mech. Rev. , vol.47
    • Kachanov, M.1    Tsukrov, I.2    Shafiro, B.3
  • 40
    • 13544254011 scopus 로고
    • Berechnung der elastichen konstanten des vielkristalls aus den konstanten des einkristalls
    • Kröner, E. (1958) Berechnung der elastichen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Z. Physik 151, 504-518.
    • (1958) Z. Physik , vol.151 , pp. 504-518
    • Kröner, E.1
  • 41
    • 0039694029 scopus 로고
    • Interacting arbitrarily oriented cracks in anisotropic matrix. Stress intensity factors and effective moduli
    • Mauge, C. and Kachanov, M. (1992) Interacting arbitrarily oriented cracks in anisotropic matrix. Stress intensity factors and effective moduli. Int. J. Fracture 58, R69-R74.
    • (1992) Int. J. Fracture , vol.58
    • Mauge, C.1    Kachanov, M.2
  • 42
    • 0028422355 scopus 로고
    • Effective elastic properties of an anisotropic material with arbitrarily oriented interacting cracks
    • Mauge, C. and Kachanov, M. (1994) Effective elastic properties of an anisotropic material with arbitrarily oriented interacting cracks. J. Mech. Phys. Solids 42, 561-584.
    • (1994) J. Mech. Phys. Solids , vol.42 , pp. 561-584
    • Mauge, C.1    Kachanov, M.2
  • 43
    • 0015625688 scopus 로고
    • Average stress in matrix and average elastic energy of materials with misfitting inclusions
    • Mori, T. and Tanaka, K. (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571-574.
    • (1973) Acta Metall. , vol.21 , pp. 571-574
    • Mori, T.1    Tanaka, K.2
  • 44
    • 0027167171 scopus 로고
    • Solids with periodically distributed cracks
    • Nemat-Nasser, S. and Yu, N. (1993) Solids with periodically distributed cracks. Int. J. Solids Structures 30, 2071-2095.
    • (1993) Int. J. Solids Structures , vol.30 , pp. 2071-2095
    • Nemat-Nasser, S.1    Yu, N.2
  • 45
    • 0026169311 scopus 로고
    • Microplane model for triaxial deformation of saturated cohesive soils
    • Prat, P. C. and Bažant, Z. P. (1991) Microplane model for triaxial deformation of saturated cohesive soils. ASCE J. Geotech. Engng 117, 891-912.
    • (1991) ASCE J. Geotech. Engng , vol.117 , pp. 891-912
    • Prat, P.C.1    Bažant, Z.P.2
  • 46
    • 0000004138 scopus 로고
    • The viscosity of suspensions of rigid spheres
    • Roscoe, R. A. (1952) The viscosity of suspensions of rigid spheres. Brit. J. Appl. Phys. 3, 267-269.
    • (1952) Brit. J. Appl. Phys. , vol.3 , pp. 267-269
    • Roscoe, R.A.1
  • 48
    • 0025782183 scopus 로고
    • A simple technique for finding effective elastic constants of cracked solids for arbitrary crack orientation statistics
    • Sayers, C. M. and Kachanov, M. (1991) A simple technique for finding effective elastic constants of cracked solids for arbitrary crack orientation statistics. Int. J. Solids Structures 27, 671-680.
    • (1991) Int. J. Solids Structures , vol.27 , pp. 671-680
    • Sayers, C.M.1    Kachanov, M.2
  • 49
    • 0029530006 scopus 로고
    • Microcrack-induced elastic wave anisotropy of brittle rocks
    • Sayers, C. M. and Kachanov, M. (1995) Microcrack-induced elastic wave anisotropy of brittle rocks. J. Geophys. Res. 100(B3). 4149-4156.
    • (1995) J. Geophys. Res. , vol.100 , Issue.B3 , pp. 4149-4156
    • Sayers, C.M.1    Kachanov, M.2
  • 51
    • 0001329717 scopus 로고
    • Continuum theory of medium with cracks
    • Vakulenko, A. A. and Kachanov, M. (1971) Continuum theory of medium with cracks. Mech. Solids 6, 145-151.
    • (1971) Mech. Solids , vol.6 , pp. 145-151
    • Vakulenko, A.A.1    Kachanov, M.2
  • 52
    • 0022203936 scopus 로고
    • The effect of microcracks on the elastic moduli of brittle materials
    • Zimmerman, R. W. (1985) The effect of microcracks on the elastic moduli of brittle materials. J. Mater. Sci. Lett. 4, 1457-1460.
    • (1985) J. Mater. Sci. Lett. , vol.4 , pp. 1457-1460
    • Zimmerman, R.W.1


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