Residual Stress and Structural Anisotropy of Cortical Bone

  • Shigeru TadanoEmail author
  • Satoshi Yamada
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


The concept of residual stress and strain does not have long history for biological tissues. In the case of cortical bone, during remodeling process the old tissue is replaced by the new tissue with construction of osteons. Since the new tissue is generated under in vivo loadings as a non-deformed state, an indeterminate structure may be generated as a result of difference between the deformations of the old and new phases. Further, the mechanical properties (e.g. elastic modulus) are also different in these phases. Because of such non-uniform structures in cortical bone, residual stress/strain will remain in the replaced region even without external loading being applied. Tadano and co-workers initiated efforts to estimate residual stress/strain in cortical bone. In a very few applications with bone, the authors have successfully applied X-ray diffraction to quantify residual stresses at the bone surface. In this work, site-specific residual strain characteristics in relation with the mineral crystal orientation were studied and the sin2 ψ method was applied to measure residual stresses in bovine and rabbit extremities. The relationship between residual stress and osteon population density on the respective sites has also been obtained. Thus the knowledge about residual stress/strain in cortical bone, related with mineral crystal distribution and osteon population density, might play an important role in the biomechanical aspects of bone healing and remodeling.


Biomechanics Cortical bone Residual stress Structural anisotropy X-ray diffraction 


  1. 1.
    Tadano S, Okoshi T (2006) Residual stress in bone structure and tissue of rabbit’s tibiofibula. Bio-Med Mater Eng 16:11–21Google Scholar
  2. 2.
    Tadano S, Giri B (2011) X-ray diffraction as a promising tool to characterize bone nanocomposites. Sci Technol Adv Mater 12:064708 (11pp)CrossRefGoogle Scholar
  3. 3.
    Fujisaki K, Tadano S, Sasaki N (2006) A method on strain measurement of HAp in cortical bone from diffusive profile of X-ray diffraction. J Biomech 39:579–586CrossRefGoogle Scholar
  4. 4.
    Fujisaki K, Tadano S (2007) Relationship between bone tissue strain and lattice strain of HAp crystals in bovine cortical bone under tensile loading. J Biomech 40:1832–1838CrossRefGoogle Scholar
  5. 5.
    Tadano S, Giri B, Sato T, Fujisaki K, Todoh M (2008) Estimating nanoscale deformation in bone by X-ray diffraction imaging method. J Biomech 41:945–952CrossRefGoogle Scholar
  6. 6.
    Giri B, Tadano S, Fujisaki K, Todoh M (2008) Understanding site-specific residual strain and architecture in bovine cortical bone. J Biomech 41:3107–3115CrossRefGoogle Scholar
  7. 7.
    Yamada S, Tadano S (2010) Residual stress around the cortical surface in bovine femoral diaphysis. J Biomech Eng 132:044503CrossRefGoogle Scholar
  8. 8.
    Yamada S, Tadano S, Todoh M, Fujisaki K (2011) Residual stress distribution in the bovine femoral diaphysis measured by synchrotron. J Biomech Sci Eng 6:114–124CrossRefGoogle Scholar
  9. 9.
    Gibson VA, Stover SM, Gibeling JC, Hazelwood SJ, Martin RB (2006) Osteonal effects on elastic modulus and fatigue life in equine bone. J Biomech 39:217–225CrossRefGoogle Scholar
  10. 10.
    Rho JY, Zioupos P, Currey JD, Pharr GM (1999) Variations in the individual thick lamellar properties within osteons by nanoindentation. Bone 25:295–300CrossRefGoogle Scholar
  11. 11.
    Yamada S, Tadano S, Fujisaki K (2011) Residual stress distribution in rabbit limb bones. J Biomech 44:1285–1290CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2014

Authors and Affiliations

  1. 1.Division of Human Mechanical Systems and Design, Faculty of EngineeringHokkaido UniversitySapporoJapan

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