1932

Abstract

The mechanical properties of bone are fundamental to the ability of our skeletons to support movement and to provide protection to our vital organs. As such, deterioration in mechanical behavior with aging and/or diseases such as osteoporosis and diabetes can have profound consequences for individuals’ quality of life. This article reviews current knowledge of the basic mechanical behavior of bone at length scales ranging from hundreds of nanometers to tens of centimeters. We present the basic tenets of bone mechanics and connect them to some of the arcs of research that have brought the field to recent advances. We also discuss cortical bone, trabecular bone, and whole bones, as well as multiple aspects of material behavior, including elasticity, yield, fracture, fatigue, and damage. We describe the roles of bone quantity (e.g., density, porosity) and bone quality (e.g., cross-linking, protein composition), along with several avenues of future research.

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2018-06-04
2024-04-26
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Literature Cited

  1. 1.  McElhaney JH 1966. Dynamic response of bone and muscle tissue. J. Appl. Physiol. 21:1231–36
    [Google Scholar]
  2. 2.  Zioupos P, Hansen U, Currey JD 2008. Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure. J. Biomech. 41:2932–39
    [Google Scholar]
  3. 3.  Fondrk MT, Bahniuk EH, Davy DT 1999. A damage model for nonlinear tensile behavior of cortical bone. J. Biomech. Eng. 121:533–41
    [Google Scholar]
  4. 4.  Frost HM 1960. Presence of microscopic cracks in vivo in bone. Henry Ford Hosp. Bull. 8:27–35
    [Google Scholar]
  5. 5.  Martin RB 2003. Fatigue microdamage as an essential element of bone mechanics and biology. Calcif. Tissue Int. 73:101–7
    [Google Scholar]
  6. 6.  Varvani-Farahani A, Najmi H 2010. A damage assessment model for cadaveric cortical bone subjected to fatigue cycles. Int. J. Fatigue 32:420–27
    [Google Scholar]
  7. 7.  Poundarik AA, Diab T, Sroga GE, Ural A, Boskey AL et al. 2012. Dilatational band formation in bone. PNAS 109:19178–83
    [Google Scholar]
  8. 8.  Jepsen KJ, Davy DT, Krzypow DJ 1999. The role of the lamellar interface during torsional yielding of human cortical bone. J. Biomech. 32:303–10
    [Google Scholar]
  9. 9.  Burr DB, Turner CH, Naick P, Forwood MR, Ambrosius W et al. 1998. Does microdamage accumulation affect the mechanical properties of bone?. J. Biomech. 31:337–45
    [Google Scholar]
  10. 10.  Nicolella DP, Ni Q, Chan KS 2011. Non-destructive characterization of microdamage in cortical bone using low field pulsed NMR. J. Mech. Behav. Biomed. Mater. 4:383–91
    [Google Scholar]
  11. 11.  Norman TL, Yeni YN, Brown CU, Wang Z 1998. Influence of microdamage on fracture toughness of the human femur and tibia. Bone 23:303–6
    [Google Scholar]
  12. 12.  Courtney AC, Hayes WC, Gibson LJ 1996. Age-related differences in post-yield damage in human cortical bone. Experiment and model. J. Biomech. 29:1463–71
    [Google Scholar]
  13. 13.  Schaffler MB, Radin EL, Burr DB 1989. Mechanical and morphological effects of strain rate on fatigue of compact bone. Bone 10:207–14
    [Google Scholar]
  14. 14.  Vashishth D, Tanner KE, Bonfield W 2000. Contribution, development and morphology of micro-cracking in cortical bone during crack propagation. J. Biomech. 33:1169–74
    [Google Scholar]
  15. 15.  Nalla RK, Stolken JS, Kinney JH, Ritchie RO 2005. Fracture in human cortical bone: local fracture criteria and toughening mechanisms. J. Biomech. 38:1517–25
    [Google Scholar]
  16. 16.  Bonfield W, Datta PK 1976. Fracture toughness of compact bone. J. Biomech. 9:131–34
    [Google Scholar]
  17. 17.  Zimmermann EA, Gludovatz B, Schaible E, Busse B, Ritchie RO 2014. Fracture resistance of human cortical bone across multiple length scales at physiological strain rates. Biomaterials 35:5472–81
    [Google Scholar]
  18. 18.  Gauthier R, Follet H, Langer M, Meille S, Chevalier J et al. 2017. Strain rate influence on human cortical bone toughness: a comparative study of four paired anatomical sites. J. Mech. Behav. Biomed. Mater. 71:223–30
    [Google Scholar]
  19. 19.  Zimmermann EA, Busse B, Ritchie RO 2015. The fracture mechanics of human bone: influence of disease and treatment. BoneKEy Rep 4:743
    [Google Scholar]
  20. 20.  Pattin CA, Caler WE, Carter DR 1996. Cyclic mechanical property degradation during fatigue loading of cortical bone. J. Biomech. 29:69–79
    [Google Scholar]
  21. 21.  Fletcher L, Codrington J, Parkinson I 2014. Effects of fatigue induced damage on the longitudinal fracture resistance of cortical bone. J. Mater. Sci. Mater. Med. 25:1661–70
    [Google Scholar]
  22. 22.  Carter DR, Hayes WC 1977. Compact bone fatigue damage—I. Residual strength and stiffness. J. Biomech. 10:325–37
    [Google Scholar]
  23. 23.  Zioupos P, Currey JD, Casinos A 2001. Tensile fatigue in bone: Are cycles-, or time to failure, or both, important?. J. Theor. Biol. 210:389–99
    [Google Scholar]
  24. 24.  Caler WE, Carter DR 1989. Bone creep–fatigue damage accumulation. J. Biomech. 22:625–35
    [Google Scholar]
  25. 25.  Lee TC, Arthur TL, Gibson LJ, Hayes WC 2000. Sequential labelling of microdamage in bone using chelating agents. J. Orthop. Res. 18:322–25
    [Google Scholar]
  26. 26.  Landrigan MD, Li J, Turnbull TL, Burr DB, Niebur GL, Roeder RK 2011. Contrast-enhanced micro–computed tomography of fatigue microdamage accumulation in human cortical bone. Bone 48:443–50
    [Google Scholar]
  27. 27.  Zysset PK, Curnier A 1996. A 3D damage model for trabecular bone based on fabric tensors. J. Biomech. 29:1549–58
    [Google Scholar]
  28. 28.  George WT, Vashishth D 2006. Susceptibility of aging human bone to mixed-mode fracture increases bone fragility. Bone 38:105–11
    [Google Scholar]
  29. 29.  Olvera D, Zimmermann EA, Ritchie RO 2012. Mixed-mode toughness of human cortical bone containing a longitudinal crack in far-field compression. Bone 50:331–36
    [Google Scholar]
  30. 30.  Cezayirlioglu H, Bahniuk E, Davy DT, Heiple KG 1985. Anisotropic yield behavior of bone under combined axial force and torque. J. Biomech. 18:61–69
    [Google Scholar]
  31. 31.  Schwiedrzik JJ, Wolfram U, Zysset PK 2013. A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales. Biomech. Model. Mechanobiol. 12:1155–68
    [Google Scholar]
  32. 32.  Arramon YP, Mehrabadi MM, Martin DW, Cowin SC 2000. A multidimensional anisotropic strength criterion based on Kelvin modes. Int. J. Solids Struct. 37:2915–35
    [Google Scholar]
  33. 33.  Ascenzi A, Baschieri P, Benvenuti A 1994. The torsional properties of single selected osteons. J. Biomech. 27:875–84
    [Google Scholar]
  34. 34.  Dong XN, Zhang X, Guo XE 2005. Interfacial strength of cement lines in human cortical bones. Mech. Chem. Biosyst. 2:63–68
    [Google Scholar]
  35. 35.  Bigley RF, Griffin LV, Christensen L, Vandenbosch R 2006. Osteon interfacial strength and histomorphometry of equine cortical bone. J. Biomech. 39:1629–40
    [Google Scholar]
  36. 36.  Rho J-Y, Tsui TY, Pharr GM 1997. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials 18:1325–30
    [Google Scholar]
  37. 37.  Franzoso G, Zysset PK 2009. Elastic anisotropy of human cortical bone secondary osteons measured by nanoindentation. J. Biomech. Eng. 131:021001
    [Google Scholar]
  38. 38.  Hoffler CE, Guo XE, Zysset PK, Goldstein SA 2005. An application of nanoindentation technique to measure bone tissue lamellae properties. J. Biomech. Eng. 127:1046–53
    [Google Scholar]
  39. 39.  Schwiedrzik J, Raghavan R, Burki A, LeNader V, Wolfram U et al. 2014. In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone. Nat. Mater. 13:740–47
    [Google Scholar]
  40. 40.  Tertuliano OA, Greer JR 2016. The nanocomposite nature of bone drives its strength and damage resistance. Nat. Mater. 15:1195–202
    [Google Scholar]
  41. 41.  Kataruka A, Mendu K, Okeoghene O, Puthuvelil J, Akono AT 2017. Microscopic assessment of bone toughness using scratch tests. Bone Rep 6:17–25
    [Google Scholar]
  42. 42.  Schaffler MB, Burr DB 1988. Stiffness of compact bone: effects of porosity and density. J. Biomech. 21:13–16
    [Google Scholar]
  43. 43.  Behrens JC, Walker PS, Shoji H 1974. Variations in strength and structure of cancellous bone at the knee. J. Biomech. 7:201–7
    [Google Scholar]
  44. 44.  Ural A, Vashishth D 2007. Effects of intracortical porosity on fracture toughness in aging human bone: a microCT-based cohesive finite element study. J. Biomech. Eng. 129:625–31
    [Google Scholar]
  45. 45.  McCalden RW, McGeough JA, Barker MB, Court-Brown CM 1993. Age-related changes in the tensile properties of cortical bone: the relative importance of changes in porosity, mineralization and microstructure. J. Bone Joint Surg. 75:A1193–205
    [Google Scholar]
  46. 46.  Turnbull TL, Baumann AP, Roeder RK 2014. Fatigue microcracks that initiate fracture are located near elevated intracortical porosity but not elevated mineralization. J. Biomech. 47:3135–42
    [Google Scholar]
  47. 47.  Kovacs CS 2017. The skeleton is a storehouse of mineral that is plundered during lactation and (fully?) replenished afterwards. J. Bone Miner. Res. 32:676–80
    [Google Scholar]
  48. 48.  Lloyd AA, Gludovatz B, Riedel C, Luengo EA, Saiyed R et al. 2017. Atypical fracture with long-term bisphosphonate therapy is associated with altered cortical composition and reduced fracture resistance. PNAS 114:8722–27
    [Google Scholar]
  49. 49.  Vashishth D, Gibson GJ, Khoury JI, Schaffler MB, Kimura J, Fyhrie DP 2001. Influence of nonenzymatic glycation on biomechanical properties of cortical bone. Bone 28:195–201
    [Google Scholar]
  50. 50.  Boskey AL 2013. Bone composition: relationship to bone fragility and antiosteoporotic drug effects. BoneKEy Rep 2:447
    [Google Scholar]
  51. 51.  Mandair GS, Morris MD 2015. Contributions of Raman spectroscopy to the understanding of bone strength. BoneKEy Rep 4:620
    [Google Scholar]
  52. 52.  Buckley K, Kerns JG, Vinton J, Gikas PD, Smith C et al. 2015. Towards the in vivo prediction of fragility fractures with Raman spectroscopy. J. Raman Spectrosc. 46:610–18
    [Google Scholar]
  53. 53.  Jager I, Fratzl P 2000. Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys. J. 79:1737–46
    [Google Scholar]
  54. 54.  Yuan F, Stock SR, Haeffner DR, Almer JD, Dunand DC, Brinson LC 2011. A new model to simulate the elastic properties of mineralized collagen fibril. Biomech. Model. Mechanobiol. 10:147–60
    [Google Scholar]
  55. 55.  Nair AK, Gautieri A, Buehler MJ 2014. Role of intrafibrillar collagen mineralization in defining the compressive properties of nascent bone. Biomacromolecules 15:2494–500
    [Google Scholar]
  56. 56.  Abueidda DW, Sabet FA, Jasiuk IM 2017. Modeling of stiffness and strength of bone at nanoscale. J. Biomech. Eng. 139:051006
    [Google Scholar]
  57. 57.  Pidaparti RMV, Chandran A, Takano Y, Turner CH 1996. Bone mineral lies mainly outside collagen fibrils: predictions of a composite model for osternal bone. J. Biomech. 29:909–16
    [Google Scholar]
  58. 58.  Katz JL 1980. Anisotropy of Young's modulus of bone. Nature 283:106–7
    [Google Scholar]
  59. 59.  Hellmich C, Barthelemy J, Dormieux L 2004. Mineral-collagen interactions in elasticity of bone ultrastructure—a continuum micromechanics approach. Eur. J. Mech. A 23:783–810
    [Google Scholar]
  60. 60.  Deuerling JM, Yue W, Espinoza Orias AA, Roeder RK 2009. Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone. J. Biomech. 42:2061–67
    [Google Scholar]
  61. 61.  Yoon YJ, Cowin SC 2008. The estimated elastic constants for a single bone osteonal lamella. Biomech. Model. Mechanobiol. 7:1–11
    [Google Scholar]
  62. 62.  Sansalone V, Naili S, Bousson V, Bergot C, Peyrin F et al. 2010. Determination of the heterogeneous anisotropic elastic properties of human femoral bone: from nanoscopic to organ scale. J. Biomech. 43:1857–63
    [Google Scholar]
  63. 63.  Martínez-Reina J, Domínguez J, García-Aznar J 2010. Effect of porosity and mineral content on the elastic constants of cortical bone: a multiscale approach. Biomech. Model. Mechanobiol. 10:309–22
    [Google Scholar]
  64. 64.  Currey JD, Brear K, Zioupos P 1996. The effects of ageing and changes in mineral content in degrading the toughness of human femora. J. Biomech. 29:257–60
    [Google Scholar]
  65. 65.  Wang X, Shen X, Li X, Mauli Agrawal C 2002. Age-related changes in the collagen network and toughness of bone. Bone 31:1–7
    [Google Scholar]
  66. 66.  Sroga GE, Vashishth D 2012. Effects of bone matrix proteins on fracture and fragility in osteoporosis. Curr. Osteoporos. Rep. 10:141–50
    [Google Scholar]
  67. 67.  Nalla RK, Kruzic JJ, Kinney JH, Ritchie RO 2004. Effect of aging on the toughness of human cortical bone: evaluation by R-curves. Bone 35:1240–46
    [Google Scholar]
  68. 68.  Burstein A, Reilly D, Martens M 1976. Aging of bone tissue: mechanical properties. J. Bone Joint Surg. Am. 58:82–86
    [Google Scholar]
  69. 69.  Koester KJ, Barth HD, Ritchie RO 2011. Effect of aging on the transverse toughness of human cortical bone: evaluation by R-curves. J. Mech. Behav. Biomed. Mater. 4:1504–13
    [Google Scholar]
  70. 70.  Campbell GM, Tiwari S, Picke AK, Hofbauer C, Rauner M et al. 2016. Effects of insulin therapy on porosity, non-enzymatic glycation and mechanical competence in the bone of rats with type 2 diabetes mellitus. Bone 91:186–93
    [Google Scholar]
  71. 71.  Brock GR, Chen JT, Ingraffea AR, MacLeay J, Pluhar GE et al. 2015. The effect of osteoporosis treatments on fatigue properties of cortical bone tissue. Bone Rep 2:8–13
    [Google Scholar]
  72. 72.  Allen MR, Burr DB 2011. Bisphosphonate effects on bone turnover, microdamage, and mechanical properties: what we think we know and what we know that we don't know. Bone 49:56–65
    [Google Scholar]
  73. 73.  Chapurlat RD, Delmas PD 2009. Bone microdamage: a clinical perspective. Osteoporos. Int. 20:1299–308
    [Google Scholar]
  74. 74.  Nyman JS, Even JL, Jo CH, Herbert EG, Murry MR et al. 2011. Increasing duration of type 1 diabetes perturbs the strength–structure relationship and increases brittleness of bone. Bone 48:733–40
    [Google Scholar]
  75. 75.  Rubin MR, Paschalis EP, Poundarik A, Sroga GE, McMahon DJ et al. 2016. Advanced glycation endproducts and bone material properties in type 1 diabetic mice. PLOS ONE 11:e0154700
    [Google Scholar]
  76. 76.  Carriero A, Zimmermann EA, Paluszny A, Tang SY, Bale H et al. 2014. How tough is brittle bone? Investigating osteogenesis imperfecta in mouse bone. J. Bone Miner. Res. 29:1392–401
    [Google Scholar]
  77. 77.  Heveran CM, Ortega AM, Cureton A, Clark R, Livingston EW et al. 2016. Moderate chronic kidney disease impairs bone quality in C57Bl/6J mice. Bone 86:1–9
    [Google Scholar]
  78. 78.  Keaveny TM, Wachtel EF, Ford CM, Hayes WC 1994. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J. Biomech. 27:1137–46
    [Google Scholar]
  79. 79.  Morgan EF, Yeh OC, Chang WC, Keaveny TM 2001. Nonlinear behavior of trabecular bone at small strains. J. Biomech. Eng. 123:1–9
    [Google Scholar]
  80. 80.  Keaveny TM, Wachtel EF, Kopperdahl DL 1999. Mechanical behavior of human trabecular bone after overloading. J. Orthop. Res. 17:346–53
    [Google Scholar]
  81. 81.  Kopperdahl DL, Pearlman JL, Keaveny TM 2000. Biomechanical consequences of an isolated overload on the human vertebral body. J. Orthop. Res. 18:685–90
    [Google Scholar]
  82. 82.  Morgan EF, Keaveny TM 2001. Dependence of yield strain of human trabecular bone on anatomic site. J. Biomech. 24:569–77
    [Google Scholar]
  83. 83.  Hildebrand T, Laib A, Müller R, Dequeker J, Rüegsegger P 1999. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J. Bone Miner. Res. 14:1167–74
    [Google Scholar]
  84. 84.  Whitehouse WJ 1974. The quantitative morphology of anisotropic trabecular bone. J. Microsc. 2:153–68
    [Google Scholar]
  85. 85.  Harrigan T, Mann R 1984. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci. 19:761–67
    [Google Scholar]
  86. 86.  Cowin SC 1985. The relationship between the elasticity tensor and the fabric tensor. Mech. Mater. 4:137–47
    [Google Scholar]
  87. 87.  Banse X, Deogelaer JP, Munting E, Delloye C, Cornu O, Grynpas M 2001. Inhomogeneity of human vertebral cancellous bone: systematic density and structure patterns inside the vertebral body. Bone 28:563–71
    [Google Scholar]
  88. 88.  Goldstein SA, Wilson DL, Matthews LS 1983. The mechanical properties of human tibial trabecular bone as a function of metaphyseal location. J. Biomech. 16:965–69
    [Google Scholar]
  89. 89.  Ciarelli MJ, Goldstein SA, Kuhn JL, Cody DD, Brown MB 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. 9:674–82
    [Google Scholar]
  90. 90.  Carter DR, Hayes WC 1976. Bone compressive strength: the influence of density and strain rate. Science 194:1174–76
    [Google Scholar]
  91. 91.  Morgan EF, Bayraktar HH, Keaveny TM 2003. Trabecular bone modulus–density relationships depend on anatomic site. J. Biomech. 36:897–904
    [Google Scholar]
  92. 92.  Mosekilde L, Mosekilde LE, Danielsen CC 1987. Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals. Bone 8:79–85
    [Google Scholar]
  93. 93.  Odgaard A, Kabel J, van Rietbergen B, Dalstra M, Huiskes R 1997. Fabric and elastic principal directions of cancellous bone are closely related. J. Biomech. 30:487–95
    [Google Scholar]
  94. 94.  Yang G, Kabel J, van Rietbergen B, Odgaard A, Huiskes R 1999. The anisotropic Hooke's law for cancellous bone and wood. J. Elast. 53:125–46
    [Google Scholar]
  95. 95.  Zysset PK, Goulet RW, Hollister SJ 1998. A global relationship between trabecular bone morphology and homogenized elastic properties. J. Biomech. Eng. 120:640–46
    [Google Scholar]
  96. 96.  Unnikrishnan GU, Gallagher JA, Hussein AI, Barest GD, Morgan EF 2015. Elastic anisotropy of trabecular bone in the elderly human vertebra. J. Biomech. Eng. 137:114503
    [Google Scholar]
  97. 97.  Chang WCW, Christensen TM, Pinilla TP, Keaveny TM 1999. Uniaxial yield strains for bovine trabecular bone are isotropic and asymmetric. J. Orthop. Res. 17:582–85
    [Google Scholar]
  98. 98.  Bevill G, Farhamand F, Keaveny TM 2009. Heterogeneity of yield strain in low-density versus high-density human trabecular bone. J. Biomech. 42:2165–70
    [Google Scholar]
  99. 99.  Turner CH 1989. Yield behavior of bovine cancellous bone. J. Biomech. Eng. 111:256–60
    [Google Scholar]
  100. 100.  Linde F, Norgaard P, Hvid I, Odgaard A, Soballe K 1991. Mechanical properties of trabecular bone. Dependency on strain rate. J. Biomech. 24:803–9
    [Google Scholar]
  101. 101.  Carter DR, Hayes WC 1977. The compressive behavior of bone as a two-phase porous structure. J. Bone Joint Surg. 59:954–62
    [Google Scholar]
  102. 102.  Burgers TA, Lakes RS, Garcia-Rodriguez S, Pill GR, Ploeg HL 2009. Post-yield relaxation behavior of bovine cancellous bone. J. Biomech. 42:2728–33
    [Google Scholar]
  103. 103.  Bowman SM, Keaveny TM, Gibson LJ, Hays WC, McMahon TA 1994. Compressive creep behavior of bovine trabecular bone. J. Biomech. 27:301–5
    [Google Scholar]
  104. 104.  Fyhrie DP, Schaffler MB 1994. Failure mechanisms in human vertebral cancellous bone. Bone 15:105–9
    [Google Scholar]
  105. 105.  Nagaraja S, Couse TL, Guldberg RE 2005. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J. Biomech. 38:707–16
    [Google Scholar]
  106. 106.  Tang SY, Vashishth D 2007. A non-invasive in vitro technique for the three-dimensional quantification of microdamage in trabecular bone. Bone 40:1259–64
    [Google Scholar]
  107. 107.  Goff MG, Lambers FM, Sorna RM, Keaveny TM, Hernandez CJ 2015. Finite element models predict the location of microdamage in cancellous bone following uniaxial loading. J. Biomech. 48:4142–48
    [Google Scholar]
  108. 108.  Jungmann R, Szabo ME, Schitter G, Tang RU, Vashishth D et al. 2011. Local strain and damage mapping in single trabeculae during three-point bending tests. J. Mech. Behav. Biomed. Mater. 4:523–34
    [Google Scholar]
  109. 109.  Morgan EF, Yeh OC, Keaveny TM 2005. Damage in trabecular bone at small strains. Eur. J. Morphol. 42:13–21
    [Google Scholar]
  110. 110.  Lambers FM, Bouman AR, Tkachenko EV, Keaveny TM, Hernandez CJ 2014. The effects of tensile-compressive loading mode and microarchitecture on microdamage in human vertebral cancellous bone. J. Biomech. 47:3605–12
    [Google Scholar]
  111. 111.  Arlot ME, Burt-Pichat B, Rouz JP, Vashishth D, Bouxsein ML, Delmas PD 2008. Microarchitecture influences microdamage accumulation in human vertebral trabecular bone. J. Bone Miner. Res. 23:1613–18
    [Google Scholar]
  112. 112.  Shi XT, Liu XS, Wang X, Guo XE, Niebur GL 2010. Type and orientation of yielded trabeculae during overloading of trabecular bone along orthogonal directions. J. Biomech. 43:2460–66
    [Google Scholar]
  113. 113.  Cook RB, Zioupos P 2009. The fracture toughness of cancellous bone. J. Biomech. 42:2054–60
    [Google Scholar]
  114. 114.  Moore TLA, Gibson LJ 2003. Fatigue microdamage in bovine trabecular bone. J. Biomech. Eng. 125:769–76
    [Google Scholar]
  115. 115.  Yamamoto E, Crawford RP, Chan DD, Keaveny TM 2006. Development of residual strains in human vertebral trabecular bone after prolonged static and cyclic loadings at low load levels. J. Biomech. 39:1812–18
    [Google Scholar]
  116. 116.  Kosmopoulos V, Schizas C, Keller TS 2008. Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue. J. Biomech. 41:515–22
    [Google Scholar]
  117. 117.  Rapillard L, Charlebois M, Zysset PK 2006. Compressive fatigue behavior of human vertebral trabecular bone. J. Biomech. 39:2133–39
    [Google Scholar]
  118. 118.  Dendorfer S, Maier HJ, Taylor D, Hammer J 2008. Anisotropy of the fatigue behaviour of cancellous bone. J. Biomech. 41:636–41
    [Google Scholar]
  119. 119.  Cowin SC 1986. Fabric dependence of an anisotropic strength criterion. Mech. Mater. 5:251–60
    [Google Scholar]
  120. 120.  Pietrusczak SID, Pande GN 1999. A fabric-dependent facture criterion for bone. J. Biomech. 32:1071–79
    [Google Scholar]
  121. 121.  Zysset PK, Rincon-Kohli L 2006. An alternative fabric-based yield and failure criterion for trabecular bone. Mechanics of Biological Tissues GA Hozapfel, RW Ogden 457–70 Berlin: Springer
    [Google Scholar]
  122. 122.  Goda I, Ganghoffer JF 2015. 3D plastic collapse and brittle fracture surface models of trabecular bone from asymptotic homogenization method. Int. J. Eng. Sci. 87:58–82
    [Google Scholar]
  123. 123.  Levrero-Florencio F, Margetts L, Sales E, Xie S, Manda K, Pankaj P 2016. Evaluating the macroscopic yield behaviour of trabecular bone using a nonlinear homogenisation approach. J. Mech. Behav. Biomed. Mater. 61:384–96
    [Google Scholar]
  124. 124.  Garcia D, Zysset PK, Charlebois M, Curnier A 2009. A three-dimensional elastic plastic damage constitutive law for bone tissue. Biomech. Model. Mechanobiol. 8:149–65
    [Google Scholar]
  125. 125.  Charlebois M, Jirasek M, Zysset PK 2010. A nonlocal constitutive model for trabecular bone softening in compression. Biomech. Model. Mechanobiol. 9:597–611
    [Google Scholar]
  126. 126.  Gibson LJ, Ashby MF 1997. Cancellous bone. Cellular Solids: Structure and Properties429–52 Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  127. 127.  Gibson LJ 2005. Biomechanics of cellular solids. J. Biomech. 38:377–99
    [Google Scholar]
  128. 128.  Turner CH, Cowin SC 1987. Dependence of elastic constants of an anisotropic porous material upon porosity and fabric. J. Mater. Sci. 22:3178–84
    [Google Scholar]
  129. 129.  Zysset PK, Curnier A 1995. An alternative model for anisotropic elasticity based on fabric tensors. Mech. Mater. 21:243–50
    [Google Scholar]
  130. 130.  Matsuura M, Eckstein F, Lochmuller EM, Zysset PK 2008. The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations. Biomech. Model. Mechanobiol. 7:27–42
    [Google Scholar]
  131. 131.  Silva MJ, Gibson LJ 1997. The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids Int. . J. Mech. Sci. 39:549–63
    [Google Scholar]
  132. 132.  van Rietbergen B, Weinans H, Huiskes R, Odgaard A 1995. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J. Biomech 28:69–81
    [Google Scholar]
  133. 133.  Kabel J, van Rietbergen B, Odgaard A, Huiskes R 1999. Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. Bone 25:481–86
    [Google Scholar]
  134. 134.  Liu XS, Sajda P, Saha PK, Wehrli FW, Guo XE 2006. Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone. J. Bone Miner. Res. 21:1608–17
    [Google Scholar]
  135. 135.  Pauchard Y, Mattmann C, Kuhn A, Gasser JA, Boyd SK 2008. European Society of Biomechanics S.M. Perren Award 2008: Using temporal trends of 3D bone micro-architecture to predict bone quality. J. Biomech. 41:2946–53
    [Google Scholar]
  136. 136.  Carretta R, Luisier B, Bernoulli D, Stussi E, Muller R, Lorenzetti S 2013. Novel method to analyze post-yield mechanical properties at trabecular bone tissue level. J. Mech. Behav. Biomed. Mater. 20:6–18
    [Google Scholar]
  137. 137.  Rho JY, Ashmann RB, Turner CH 1993. Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J. Biomech. 26:111–19
    [Google Scholar]
  138. 138.  Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM 1999. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J. Biomech 32:437–41
    [Google Scholar]
  139. 139.  Lietniewski J 2005. Determination of the elasticity coefficient for a single trabecula of a cancellous bone: scanning acoustic microscopy approach. Ultrasound Med. Biol. 31:1361–66
    [Google Scholar]
  140. 140.  Carretta R, Stussi E, Muller R, Lorenzetti S 2015. Prediction of local ultimate strain and toughness of trabecular bone tissue by Raman material composition analysis. Biomed. Res. Int. 2015:457371
    [Google Scholar]
  141. 141.  Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM 2000. High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J. Biomech 33:1575–83
    [Google Scholar]
  142. 142.  Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM 2004. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J. Biomech 37:27–35
    [Google Scholar]
  143. 143.  Choi K, Goldstein SA 1992. A comparison of the fatigue behavior of human trabecular and cortical bone tissue. J. Biomech. 25:1371–81
    [Google Scholar]
  144. 144.  Torres AM, Matheny JB, Keaveny TM, Taylor D, Rimnac CM, Hernandez CJ 2016. Material heterogeneity in cancellous bone promotes deformation recovery after mechanical failure. PNAS 113:2892–97
    [Google Scholar]
  145. 145.  Ding M, Odgaard A, Linde F, Hvid I 2002. Age-related variations in the microstructure of human tibial cancellous bone. J. Orthop. Res. 20:615–21
    [Google Scholar]
  146. 146.  Mosekilde L 1989. Sex differences in age-related loss of vertebral trabecular bone mass and structure–biomechanical consequences. Bone 10:425–32
    [Google Scholar]
  147. 147.  McCalden RW, McGeough JA, Court-Brown CM 1997. Age-related changed in the compressive strength of cancellous bone. The relative importance of changes in density and trabecular architecture. J. Bone Joint Surg. Am. Ed. 79:421–27
    [Google Scholar]
  148. 148.  Ding M, Odgaard A, Hvid I 2003. Changes in the three-dimensional microstructure of human tibial cancellous bone in early osteoarthritis. J. Bone Joint Surg. Br. 85:906–12
    [Google Scholar]
  149. 149.  Hunter DJ, Gerstenfeld L, Bishop G, Davis AD, Mason ZD et al. 2009. Bone marrow lesions from osteoarthritis knees are characterized by sclerotic bone that is less well mineralized. Arthritis Res. Ther. 11:R11
    [Google Scholar]
  150. 150.  Hong J, Cabe GD, Tedrow JR, Hipp JA, Snyder BD 2004. Failure of trabecular bone with simulated lytic defects can be predicted non-invasively by structural analysis. J. Orthop. Res. 22:479–86
    [Google Scholar]
  151. 151.  Hussein AI, Jackman TM, Morgan SR, Barest GD, Morgan EF 2013. The intra-vertebral distribution of bone density: correspondence to intervertebral disc health and implications for vertebral strength. Osteoporos. Int. 24:3021–30
    [Google Scholar]
  152. 152.  Levenston ME, Beaupré GS, van der Meulen MC 1994. Improved method for analysis of whole bone torsion tests. J. Bone Miner. Res. 9:1459–65
    [Google Scholar]
  153. 153.  Ruff CB, Hayes WC 1982. Subperiosteal expansion and cortical remodeling of the human femur and tibia with aging. Science 217:945–48
    [Google Scholar]
  154. 154.  Riggs BL, Melton LJ3rd, Robb RA, Camp JJ, Atkinson EJ et al. 2004. Population-based study of age and sex differences in bone volumetric density, size, geometry, and structure at different skeletal sites. J. Bone Miner. Res. 19:1945–54
    [Google Scholar]
  155. 155.  Keaveny TM, Kopperdahl DL, Melton LJ3rd, Hoffmann PF, Amin S et al. 2010. Age-dependence of femoral strength in white women and men. J. Bone Miner. Res. 25:994–1001
    [Google Scholar]
  156. 156.  Rezaei A, Dragomir-Daescu D 2015. Femoral strength changes faster with age than BMD in both women and men: a biomechanical study. J. Bone Miner. Res. 30:2200–6
    [Google Scholar]
  157. 157.  Courtney AC, Wachtel EF, Myers ER, Hayes WC 1995. Age-related reductions in the strength of the femur tested in a fall-loading configuration. J. Bone Joint Surg. 77:387–95
    [Google Scholar]
  158. 158.  Duan Y, Turner CH, Kim BT, Seeman E 2001. Sexual dimorphism in vertebral fragility is more the result of gender differences in age-related bone gain than bone loss. J. Bone Miner. Res. 16:2267–75
    [Google Scholar]
  159. 159.  Christiansen BA, Kopperdahl DL, Kiel DP, Keaveny TM, Bouxsein ML 2011. Mechanical contributions of the cortical and trabecular compartments contribute to differences in age-related changes in vertebral body strength in men and women assessed by QCT-based finite element analysis. J. Bone Miner. Res. 26:974–83
    [Google Scholar]
  160. 160.  Samelson EJ, Christiansen BA, Demissie S, Broe KE, Louie-Gao Q et al. 2012. QCT measures of bone strength at the thoracic and lumbar spine: the Framingham study. J. Bone Miner. Res. 27:654–63
    [Google Scholar]
  161. 161.  Kaptoge S, Beck TJ, Reeve J, Stone KL, Hillier TA et al. 2008. Prediction of incident hip fracture risk by femur geometry variables measured by hip structural analysis in the study of osteoporotic fractures. J. Bone Miner. Res. 23:1892–904
    [Google Scholar]
  162. 162.  Bouxsein ML, Karasik D 2006. Bone geometry and skeletal fragility. Curr. Osteoporos. Rep. 4:49–56
    [Google Scholar]
  163. 163.  Roux JP, Wegrzyn J, Arlot ME, Guyen O, Delmas PD et al. 2010. Contribution of trabecular and cortical components to biomechanical behavior of human vertebrae: an ex vivo study. J. Bone Miner. Res. 25:356–61
    [Google Scholar]
  164. 164.  Nekkanty S, Yerramshetty J, Kim DG, Zauel R, Johnson E et al. 2010. Stiffness of the endplate boundary layer and endplate surface topography are associated with brittleness of human whole vertebral bodies. Bone 47:783–89
    [Google Scholar]
  165. 165.  Heilmeier U, Cheng K, Pasco C, Parrish R, Nirody J et al. 2016. Cortical bone laminar analysis reveals increased midcortical and periosteal porosity in type 2 diabetic postmenopausal women with history of fragility fractures compared to fracture-free diabetics. Osteoporos. Int. 27:2791–802
    [Google Scholar]
  166. 166.  Osima M, Kral R, Borgen TT, Hogestol IK, Joakimsen RM et al. 2017. Women with type 2 diabetes mellitus have lower cortical porosity of the proximal femoral shaft using low-resolution CT than nondiabetic women, and increasing glucose is associated with reduced cortical porosity. Bone 97:252–60
    [Google Scholar]
  167. 167.  Nilsson AG, Sundh D, Johansson L, Nilsson M, Mellstrom D et al. 2017. Type 2 diabetes mellitus is associated with better bone microarchitecture but lower bone material strength and poorer physical function in elderly women: a population-based study. J. Bone Miner. Res. 32:1062–71
    [Google Scholar]
  168. 168.  Reilly DT, Burstein AH 1975. The elastic and ultimate properties of compact bone tissue. J. Biomech. 8:393–96
    [Google Scholar]
  169. 169.  Mirzaali MJ, Schwiedrzik JJ, Thaiwichai S, Best JP, Michler J et al. 2016. Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly. Bone 93:196–211
    [Google Scholar]
  170. 170.  Dong XN, Acuna RL, Luo Q, Wang X 2012. Orientation dependence of progressive post-yield behavior of human cortical bone in compression. J. Biomech. 45:2829–34
    [Google Scholar]
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