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Volumn 29, Issue 12, 1996, Pages 1549-1558

A 3D damage model for trabecular bone based on fabric tensors

Author keywords

Constitutive law; Damage; Mechanical properties; Trabecular bone; Yield

Indexed keywords

ANISOTROPY; CONTINUUM MECHANICS; CRACK PROPAGATION; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; MATHEMATICAL MODELS; MECHANICAL PROPERTIES; MECHANICAL TESTING; MORPHOLOGY; TENSORS; THREE DIMENSIONAL; YIELD STRESS;

EID: 0030560935     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9290(96)80006-6     Document Type: Article
Times cited : (108)

References (58)
  • 1
    • 0024892801 scopus 로고
    • Anatomical variation of orthotropic elastic moduli of the proximal human tibia
    • Ashman, R. B., Rho, J. Y. and Turner, C. H. (1989) Anatomical variation of orthotropic elastic moduli of the proximal human tibia. J. Biomechanics 22, 895-900.
    • (1989) J. Biomechanics , vol.22 , pp. 895-900
    • Ashman, R.B.1    Rho, J.Y.2    Turner, C.H.3
  • 2
    • 0001898250 scopus 로고
    • Introduction to the invariant formulation of anisotropic constitutive equations
    • Edited by Boehler, J. P., Springer, Berlin
    • Boehler, J. P. (1987) Introduction to the invariant formulation of anisotropic constitutive equations. In Applications of Tensor Functions in Solid Mechanics (Edited by Boehler, J. P.), pp. 3-65. Springer, Berlin.
    • (1987) Applications of Tensor Functions in Solid Mechanics , pp. 3-65
    • Boehler, J.P.1
  • 5
    • 0027203132 scopus 로고
    • Remodelling and the repair of fatigue damage
    • Burr, D. B. (1993) Remodelling and the repair of fatigue damage. Calcif. Tissue Int. 53 (suppl 1), S75-S81.
    • (1993) Calcif. Tissue Int. , vol.53 , Issue.SUPPL. 1
    • Burr, D.B.1
  • 6
    • 0026586120 scopus 로고
    • New approaches for interpreting projected bone densitometry data
    • Carter, D. R., Bouxsein, M. L. and Marcus, R. (1992) New approaches for interpreting projected bone densitometry data. J. Bone Miner. Res. 7, 137-145.
    • (1992) J. Bone Miner. Res. , vol.7 , pp. 137-145
    • Carter, D.R.1    Bouxsein, M.L.2    Marcus, R.3
  • 7
    • 0017741045 scopus 로고
    • Compact bone fatigue damage I Residual strength and stiffness
    • Carter, D. R. and Hayes, W. C. (1977a) Compact bone fatigue damage I Residual strength and stiffness. J. Biomechanics 10, 325-337.
    • (1977) J. Biomechanics , vol.10 , pp. 325-337
    • Carter, D.R.1    Hayes, W.C.2
  • 8
    • 0017698252 scopus 로고
    • The compressive behaviour of bone as a two phase porous structure
    • Carter, D. R. and Hayes, W. C. (1977b) The compressive behaviour of bone as a two phase porous structure. J. Bone Jt Surg. 59, 954-962.
    • (1977) J. Bone Jt Surg. , vol.59 , pp. 954-962
    • Carter, D.R.1    Hayes, W.C.2
  • 9
    • 0023978287 scopus 로고
    • Continuum damage mechanics: Part I - General concepts
    • Chaboche, J.-L. (1988a) Continuum damage mechanics: Part I - General concepts. J. Appl. Mech. 55, 59-64.
    • (1988) J. Appl. Mech. , vol.55 , pp. 59-64
    • Chaboche, J.-L.1
  • 10
    • 0023979659 scopus 로고
    • Continuum damage mechanics: Part II - Damage growth, crack initiation and crack growth
    • Chaboche, J.-L. (1988b) Continuum damage mechanics: Part II - Damage growth, crack initiation and crack growth. J. Appl. Mech. 55, 65-72.
    • (1988) J. Appl. Mech. , vol.55 , pp. 65-72
    • Chaboche, J.-L.1
  • 11
    • 0001274924 scopus 로고
    • Failure mechanisms of compact bone in bending: A microstructural analysis
    • New Orleans, Louisiana
    • Choi, K., Fyhrie, D. P. and Schaffler, M. B. (1994) Failure mechanisms of compact bone in bending: A microstructural analysis. Trans. 40th Orthop. Res. Soc. p. 425, New Orleans, Louisiana.
    • (1994) Trans. 40th Orthop. Res. Soc. , pp. 425
    • Choi, K.1    Fyhrie, D.P.2    Schaffler, M.B.3
  • 12
    • 0026990532 scopus 로고
    • A comparison of the fatigue behaviour of human trabecular and cortical bone tissue
    • Choi, K. and Goldstein, S. A. (1992) A comparison of the fatigue behaviour of human trabecular and cortical bone tissue. J. Biomechanics 25, 1371-1381.
    • (1992) J. Biomechanics , vol.25 , pp. 1371-1381
    • Choi, K.1    Goldstein, S.A.2
  • 13
    • 0026229643 scopus 로고
    • Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography
    • Ciarelli, M. J., Goldstein, S. A., Kuhn, J. L., Cody, D. D. and Brown, M. J. (1991) Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. J. Orthop. Res. 9, 674-682.
    • (1991) J. Orthop. Res. , vol.9 , pp. 674-682
    • Ciarelli, M.J.1    Goldstein, S.A.2    Kuhn, J.L.3    Cody, D.D.4    Brown, M.J.5
  • 14
    • 0022097744 scopus 로고
    • The relationship between the elasticity tensor and the fabric tensor
    • Cowin, S. C. (1985) The relationship between the elasticity tensor and the fabric tensor. Mech. Mater. 4, 137-147.
    • (1985) Mech. Mater. , vol.4 , pp. 137-147
    • Cowin, S.C.1
  • 17
    • 0027579804 scopus 로고
    • Mechanical and textural properties of pelvic trabecular bone
    • Dalstra, M., Huiskes, R., Odgaard, A. and Erning, L. v. (1993) Mechanical and textural properties of pelvic trabecular bone. J. Biomechanics 26, 523-535.
    • (1993) J. Biomechanics , vol.26 , pp. 523-535
    • Dalstra, M.1    Huiskes, R.2    Odgaard, A.3    Erning, L.V.4
  • 20
    • 0021880663 scopus 로고
    • The mechanical behaviour of cancellous bone
    • Gibson, L. J. (1985) The mechanical behaviour of cancellous bone. J. Biomechanics 18, 317-328.
    • (1985) J. Biomechanics , vol.18 , pp. 317-328
    • Gibson, L.J.1
  • 21
    • 0000400197 scopus 로고
    • Composition of trabecular and cortical bone
    • Gong, J. K., Arnold, J. S. and Cohn, H. (1964) Composition of trabecular and cortical bone. Anat. Record 149, 325-332.
    • (1964) Anat. Record , vol.149 , pp. 325-332
    • Gong, J.K.1    Arnold, J.S.2    Cohn, H.3
  • 22
    • 0028088849 scopus 로고
    • Fall severity and bone mineral density as risk factors for hip fracture in ambulatory elderly
    • Greenspan, S. L., Myers, E. R., Maitland, L. A., Resnick, N. M. and Hayes, W. C. (1994) Fall severity and bone mineral density as risk factors for hip fracture in ambulatory elderly. J. Am. Med. Ass. 271, 128-133.
    • (1994) J. Am. Med. Ass. , vol.271 , pp. 128-133
    • Greenspan, S.L.1    Myers, E.R.2    Maitland, L.A.3    Resnick, N.M.4    Hayes, W.C.5
  • 23
    • 0028371273 scopus 로고
    • Finite element modeling of damage accumulation in trabecular bone under cyclic loading
    • Guo, X. E. (1994) Finite element modeling of damage accumulation in trabecular bone under cyclic loading. J. Biomechanics 27, 145-155.
    • (1994) J. Biomechanics , vol.27 , pp. 145-155
    • Guo, X.E.1
  • 24
    • 0021388724 scopus 로고
    • Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor
    • Harrigan, T. P. and Mann, R. W. (1984) Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci. 19, 761-767.
    • (1984) J. Mater. Sci. , vol.19 , pp. 761-767
    • Harrigan, T.P.1    Mann, R.W.2
  • 26
    • 0029307657 scopus 로고
    • A more fundamental approach to damaged elastic stress-strain relations
    • He, Q.-C. and Curnier, A. (1995) A more fundamental approach to damaged elastic stress-strain relations. Int. J. Solids Structures 32, 1433-1457.
    • (1995) Int. J. Solids Structures , vol.32 , pp. 1433-1457
    • He, Q.-C.1    Curnier, A.2
  • 27
    • 0021212686 scopus 로고
    • Distribution of directional data and fabric tensor
    • Kanatani, K. (1984) Distribution of directional data and fabric tensor. Int. J. Engng Sci. 22, 149.
    • (1984) Int. J. Engng Sci. , vol.22 , pp. 149
    • Kanatani, K.1
  • 28
    • 0028504004 scopus 로고
    • Trabecular bone exhibits fully linear elastic behaviour and yields at low strains
    • Keaveny, T. M., Guo, X. E., Wachtel, E. F., McMahon, T. A. and Hayes, W. C. (1994a) Trabecular bone exhibits fully linear elastic behaviour and yields at low strains. J. Biomechanics 27, 1127-1136.
    • (1994) J. Biomechanics , vol.27 , pp. 1127-1136
    • Keaveny, T.M.1    Guo, X.E.2    Wachtel, E.F.3    McMahon, T.A.4    Hayes, W.C.5
  • 29
    • 0027131374 scopus 로고
    • A 20-year perspective on the mechanical properties of trabecular bone
    • Keaveny, T. M. and Hayes, W. C. (1993) A 20-year perspective on the mechanical properties of trabecular bone. J. Biomech. Engng 115, 534-542.
    • (1993) J. Biomech. Engng , vol.115 , pp. 534-542
    • Keaveny, T.M.1    Hayes, W.C.2
  • 30
    • 0028502929 scopus 로고
    • Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus
    • Keaveny, T. M., Wachtel, E. F., Ford, C. M. and Hayes, W. C. (1994b) Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J. Biomechanics 27, 1129-1137.
    • (1994) J. Biomechanics , vol.27 , pp. 1129-1137
    • Keaveny, T.M.1    Wachtel, E.F.2    Ford, C.M.3    Hayes, W.C.4
  • 33
    • 0024899509 scopus 로고
    • Damage mechanics
    • Krajcinovic, D. (1989) Damage mechanics. Mech. Mater. 8, 117-197.
    • (1989) Mech. Mater. , vol.8 , pp. 117-197
    • Krajcinovic, D.1
  • 34
  • 35
    • 0018421762 scopus 로고
    • Cement line motion in bone
    • Lakes, R. and Saha, S. (1979) Cement line motion in bone. Science 204, 501-503.
    • (1979) Science , vol.204 , pp. 501-503
    • Lakes, R.1    Saha, S.2
  • 36
    • 46549096589 scopus 로고
    • Coupled elasto-plasticity and damage constitutive equations
    • Lemaitre, J. (1985) Coupled elasto-plasticity and damage constitutive equations. Comput. Meths Appl. Mech. Engng 51, 31-49.
    • (1985) Comput. Meths Appl. Mech. Engng , vol.51 , pp. 31-49
    • Lemaitre, J.1
  • 38
    • 0023880239 scopus 로고
    • Mechanical properties of trabecular bone by a nondestructive testing approach
    • Linde, F., Gøthgen, C. B., Hvid, I., Pongsoipetch, B. and Bentzen, S. (1988) Mechanical properties of trabecular bone by a nondestructive testing approach. Engng Med. 17, 23-29.
    • (1988) Engng Med. , vol.17 , pp. 23-29
    • Linde, F.1    Gøthgen, C.B.2    Hvid, I.3    Pongsoipetch, B.4    Bentzen, S.5
  • 40
    • 0027575822 scopus 로고
    • Micromechanics of bone strength and fracture
    • Mammone, J. F. and Hudson, S. M. (1993) Micromechanics of bone strength and fracture. J. Biomechanics 26, 439-446.
    • (1993) J. Biomechanics , vol.26 , pp. 439-446
    • Mammone, J.F.1    Hudson, S.M.2
  • 41
    • 0020067149 scopus 로고
    • A hypothetical mechanism for the stimulation of osteonal remodelling by fatigue damage
    • Martin, R. B. and Burr, D. B. (1982) A hypothetical mechanism for the stimulation of osteonal remodelling by fatigue damage. J. Biomechanics 15, 137-139.
    • (1982) J. Biomechanics , vol.15 , pp. 137-139
    • Martin, R.B.1    Burr, D.B.2
  • 43
    • 0016072189 scopus 로고
    • Sur les matériaux élastoplastiques à écrouissage positif ou négatif
    • Nguyen, Q. S. and Bui, H. D. (1974) Sur les matériaux élastoplastiques à écrouissage positif ou négatif. J. Mécanique 13, 321-342.
    • (1974) J. Mécanique , vol.13 , pp. 321-342
    • Nguyen, Q.S.1    Bui, H.D.2
  • 44
    • 0011869333 scopus 로고
    • Estimation of structural anisotropy based on volume orientation. A new concept
    • Odgaard, A., Jensen, E. B. and Gundersen, H. J. G. (1990) Estimation of structural anisotropy based on volume orientation. A new concept. J. Microscopy 159, 335-342.
    • (1990) J. Microscopy , vol.159 , pp. 335-342
    • Odgaard, A.1    Jensen, E.B.2    Gundersen, H.J.G.3
  • 45
    • 0026406737 scopus 로고
    • An objective anisotropic elastic plastic model and algorithm applicable to bone mechanics
    • Rakotomanana, R. L. Curnier, A. and Leyvraz, P. F. (1991) An objective anisotropic elastic plastic model and algorithm applicable to bone mechanics. Eur. J. Mech. 10, 327-342.
    • (1991) Eur. J. Mech. , vol.10 , pp. 327-342
    • Rakotomanana, R.L.1    Curnier, A.2    Leyvraz, P.F.3
  • 46
    • 0016237894 scopus 로고
    • Mechanical properties of human cancellous bone in the femoral head
    • Schoenfeld, C. M., Lautenschlager, E. P. and Meyer, P. R. (1974) Mechanical properties of human cancellous bone in the femoral head. Med. Biol. Engng 12, 313-317.
    • (1974) Med. Biol. Engng , vol.12 , pp. 313-317
    • Schoenfeld, C.M.1    Lautenschlager, E.P.2    Meyer, P.R.3
  • 47
    • 0002381967 scopus 로고
    • Strain softening and dissipation: A unification of approaches
    • Edited by Mazars, J. and Bazant, Z. P., Elsevier Applied Science, London
    • Simo, J. C. (1989) Strain softening and dissipation: A unification of approaches. In Cracking and Damage (Edited by Mazars, J. and Bazant, Z. P.), pp. 440-461. Elsevier Applied Science, London.
    • (1989) Cracking and Damage , pp. 440-461
    • Simo, J.C.1
  • 48
    • 0002269389 scopus 로고
    • Multiaxial structure-property relations in trabecular bone
    • Edited by Mow, V. C., Ratcliffe, A. and Woo, S. L.-Y., Springer, New York
    • Snyder, B. D. and Hayes, W. C. (1990) Multiaxial structure-property relations in trabecular bone. In Biomechanics of Diarthrodial Joints (Edited by Mow, V. C., Ratcliffe, A. and Woo, S. L.-Y.), pp. 31-59. Springer, New York.
    • (1990) Biomechanics of Diarthrodial Joints , pp. 31-59
    • Snyder, B.D.1    Hayes, W.C.2
  • 49
    • 0021085023 scopus 로고
    • Multiaxial strength characteristics of trabecular bone
    • Stone, J. L., Beaupre, G. S. and Hayes, W. C. (1983) Multiaxial strength characteristics of trabecular bone. J. Biomechanics 16, 743-752.
    • (1983) J. Biomechanics , vol.16 , pp. 743-752
    • Stone, J.L.1    Beaupre, G.S.2    Hayes, W.C.3
  • 50
    • 0004274342 scopus 로고
    • Cambridge University Press, Cambridge
    • Suresh, S. (1991) Fatigue of Materials. Cambridge University Press, Cambridge.
    • (1991) Fatigue of Materials
    • Suresh, S.1
  • 51
    • 0024925041 scopus 로고
    • Failure surfaces for cellular materials under multiaxial loads - II. Comparison of models with experiment
    • Triantafillou, T. C., Zhang, J., Shercliff, T. L., Gibson, L. J. and Ashby, M. F. (1989) Failure surfaces for cellular materials under multiaxial loads - II. Comparison of models with experiment. Int. J. Mech. Sci. 31, 665-678.
    • (1989) Int. J. Mech. Sci. , vol.31 , pp. 665-678
    • Triantafillou, T.C.1    Zhang, J.2    Shercliff, T.L.3    Gibson, L.J.4    Ashby, M.F.5
  • 52
    • 0026551917 scopus 로고
    • On Wolfs law of trabecular architecture
    • Turner, C. (1992) On Wolfs law of trabecular architecture. J. Biomechanics 25, 1-9.
    • (1992) J. Biomechanics , vol.25 , pp. 1-9
    • Turner, C.1
  • 53
    • 0025333710 scopus 로고
    • The fabric dependance of the orthotropic elastic constants of cancellous bone
    • Turner, C. H., Cowin, S. C., Rho, J. Y., Ashman, R. B. and Rice, J. C. (1990) The fabric dependance of the orthotropic elastic constants of cancellous bone. J. Biomechanics 23, 549 561.
    • (1990) J. Biomechanics , vol.23 , pp. 549561
    • Turner, C.H.1    Cowin, S.C.2    Rho, J.Y.3    Ashman, R.B.4    Rice, J.C.5
  • 54
    • 0019216278 scopus 로고
    • Material properties of femoral cancellous bone in axial loading. Part II: Time dependent properties
    • Zilch, H., Rohlmann, A., Bergmann, G. and Kolbel, R. (1980) Material properties of femoral cancellous bone in axial loading. Part II: Time dependent properties. Arch. Orthop. Traumat. Surg. 97, 257-262.
    • (1980) Arch. Orthop. Traumat. Surg. , vol.97 , pp. 257-262
    • Zilch, H.1    Rohlmann, A.2    Bergmann, G.3    Kolbel, R.4
  • 57
    • 0029406775 scopus 로고
    • An alternative model for anisotropic elasticity based on fabric tensors
    • Zysset, P. K. and Curnier, A. (1995a) An alternative model for anisotropic elasticity based on fabric tensors. Mech. Mater. 21, 243-250.
    • (1995) Mech. Mater. , vol.21 , pp. 243-250
    • Zysset, P.K.1    Curnier, A.2
  • 58
    • 0029215602 scopus 로고
    • An alternative model for anisotropic elasticity of trabecular bone
    • Beaver Creek, Colarado
    • Zysset, P. K. and Curnier, A. (1995b) An alternative model for anisotropic elasticity of trabecular bone. Trans. Summer ASME, Beaver Creek, Colarado, p. 359.
    • (1995) Trans. Summer ASME , pp. 359
    • Zysset, P.K.1    Curnier, A.2


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