Skip to main content
SpringerLink
Log in

Is the 0.2%-Strain-Offset Approach Appropriate for Calculating the Yield Stress of Cortical Bone?

  • Original Article
  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

The 0.2% strain offset approach is mostly used to calculate the yield stress and serves as an efficient method for cross-lab comparisons of measured material properties. However, it is difficult to accurately determine the yield of the bone. Especially when computational models require accurate material parameters, clarification of the yield point is needed. We tested 24 cortical specimens harvested from six bovine femora in three-point bending mode, and 11 bovine femoral cortical specimens in the tensile mode. The Young’s modulus and yield stress for each specimen derived from the specimen-specific finite element (FE) optimization method was regarded as the most ideal constitutive parameter. Then, the strain offset optimization method was used to find the strain offset closest to the ideal yield stress for the 24 specimens. The results showed that the 0 strain offsets underestimated (− 25%) the yield stress in bending and tensile tests, while the 0.2% strain offsets overestimated the yield stress (+ 65%) in three-point bending tests. Instead, the yield stress determined by 0.007 and 0.05% strain offset for bending and tensile loading respectively, can effectively characterize the biomechanical responses of the bone, thereby helping to build an accurate FE model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

Similar content being viewed by others

References

  1. Abdel-Wahab, A. A., K. Alam, and V. V. Silberschmidt. Analysis of anisotropic viscoelastoplastic properties of cortical bone tissues. J. Mech. Behav. Biomed. Mater. 4:807–820, 2011.

    Article  PubMed  Google Scholar 

  2. Abraham, A. C., A. Agarwalla, A. Yadavalli, J. Y. Liu, and S. Y. Tang. Microstructural and compositional contributions towards the mechanical behavior of aging human bone measured by cyclic and impact reference point indentation. Bone 87:37–43, 2016.

    Article  PubMed  PubMed Central  Google Scholar 

  3. Albert, C. I., J. Jameson, and G. Harris. Design and validation of bending test method for characterization of miniature pediatric cortical bone specimens. Proc. Inst. Mech. Eng. H 227:105–113, 2012.

    Article  Google Scholar 

  4. Anderson, I. A., M. R. Mucalo, G. S. Johnson, and M. A. Lorier. The processing and characterization of animal-derived bone to yield materials with biomedical applications. Part III: material and mechanical properties of fresh and processed bovine cancellous bone. J. Mater. Sci. Mater. Med. 11:743–749, 2000.

    Article  CAS  PubMed  Google Scholar 

  5. Azcarate-Velazquez, F., R. Castillo-Oyague, L. G. Oliveros-Lopez, D. Torres-Lagares, A. J. Martinez-Gonzalez, A. Perez-Velasco, C. D. Lynch, J. L. Gutierrez-Perez, and M. A. Serrera-Figallo. Influence of bone quality on the mechanical interaction between implant and bone: a finite element analysis. J. Dent. 88:103161, 2019.

    Article  PubMed  Google Scholar 

  6. Barak, M. M., J. D. Currey, S. Weiner, and R. Shahar. Are tensile and compressive Young’s moduli of compact bone different? J. Mech. Behav. Biomed. Mater. 2:51–60, 2009.

    Article  PubMed  Google Scholar 

  7. Bayraktar, H. H., E. F. Morgan, G. L. Niebur, G. E. Morris, E. K. Wong, and T. M. Keaveny. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J. Biomech. 37:27–35, 2004.

    Article  PubMed  Google Scholar 

  8. Benoit, A., S. Guerard, B. Gillet, G. Guillot, F. Hild, D. Mitton, J. N. Perie, and S. Roux. 3D analysis from micro-MRI during in situ compression on cancellous bone. J. Biomech. 42:2381–2386, 2009.

    Article  PubMed  Google Scholar 

  9. Nowak, T. E., J. Blum, S. Kuhn, M. Welker, W. Sternstein, L. P. Mueller, and P. M. Rommens. Influence of formalin fixation on the biomechanical properties of human diaphyseal bone. Biomed. Tech. Biomed. Eng. 55:361–365, 2010.

    Google Scholar 

  10. Carpinteri, A., F. Berto, G. Fortese, C. Ronchei, D. Scorza, and S. Vantadori. Modified two-parameter fracture model for bone. Eng. Fract. Mech. 174:44–53, 2017.

    Article  Google Scholar 

  11. Carter, D. R., W. E. Caler, D. M. Spengler, and V. H. Frankel. Fatigue behavior of adult cortical bone: the influence of mean strain and strain range. Acta Orthop. Scand. 52:481–490, 1981.

    Article  CAS  PubMed  Google Scholar 

  12. Chen, Q., and G. A. Thouas. Metallic implant biomaterials. Mater. Sci. Eng. R 87:1–57, 2015.

    Article  Google Scholar 

  13. Choi, K., J. L. Kuhn, M. J. Ciarelli, and S. A. Goldstein. The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. J. Biomech. 23:1103–1113, 1990.

    Article  CAS  PubMed  Google Scholar 

  14. Cowin, S. C. Bone Mechanics Handbook. Boca Raton: CRC Press, 2001.

    Book  Google Scholar 

  15. Crammond, G., S. W. Boyd, and J. M. Dulieu-Barton. Speckle pattern quality assessment for digital image correlation. Opt. Lasers Eng. 51:1368–1378, 2013.

    Article  Google Scholar 

  16. Crowninshield, R. D., and M. H. Pope. The response of compact bone in tension at various strain rates. Ann. Biomed. Eng. 2:217–225, 1974.

    Article  Google Scholar 

  17. Currey, J. D., and K. Brear. Hardness, Young’s modulus and yield stress in mammalian mineralized tissues. J. Mater. Sci. Mater. Med. 1:14–20, 1990.

    Article  Google Scholar 

  18. Fredriksson, R., J. Shin, and C. D. Untaroiu. Potential of pedestrian protection systems—a parameter study using finite element models of pedestrian dummy and generic passenger vehicles. Traffic Injury Prev. 12:398–411, 2011.

    Article  Google Scholar 

  19. Fridoni, M., R. M. Farahani, H. Nejati, M. Salimi, S. M. Gharavi, M. Bayat, A. Amini, G. Torkman, and S. Bayat. Evaluation of the effects of LLLT on biomechanical properties of tibial diaphysis in two rat models of experimental osteoporosis by a three point bending test. Lasers Med. Sci. 30:1117–1125, 2015.

    Article  PubMed  Google Scholar 

  20. Garnero, P., O. Borel, E. Gineyts, F. Duboeuf, H. Solberg, M. L. Bouxsein, C. Christiansen, and P. D. Delmas. Extracellular post-translational modifications of collagen are major determinants of biomechanical properties of fetal bovine cortical bone. Bone 38:300–309, 2006.

    Article  CAS  PubMed  Google Scholar 

  21. Goh, J. C., E. J. Ang, and K. Bose. Effect of preservation medium on the mechanical properties of cat bones. Acta Orthop. Scand. 60:465–467, 1989.

    Article  CAS  PubMed  Google Scholar 

  22. Guan, F. J., X. Han, H. J. Mao, C. Wagner, Y. N. Yeni, and K. H. Yang. Application of optimization methodology and specimen-specific finite element models for investigating material properties of rat skull. Ann. Biomed. Eng. 39:85–95, 2011.

    Article  PubMed  Google Scholar 

  23. Haddadi, H., and S. Belhabib. Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Opt. Lasers Eng. 46:185–196, 2008.

    Article  Google Scholar 

  24. Horch, R. A., D. F. Gochberg, J. S. Nyman, and M. D. Does. Non-invasive predictors of human cortical bone mechanical properties: T2-discriminated 1H NMR compared with high resolution X-ray. PLoS ONE 6:e16359, 2011.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  25. Hu, J., K. D. Klinich, C. S. Miller, G. Nazmi, M. D. Pearlman, L. W. Schneider, and J. D. Rupp. Quantifying dynamic mechanical properties of human placenta tissue using optimization techniques with specimen-specific finite-element models. J. Biomech. Eng. 42:2528–2534, 2009.

    Article  Google Scholar 

  26. Hvid, I., and J. Jensen. Cancellous bone strength at the proximal human tibia. Eng. Med. 13:21–25, 1984.

    Article  CAS  PubMed  Google Scholar 

  27. Jämsä, T., P. Jalovaara, Z. Peng, H. K. Väänänen, and J. Tuukkanen. Comparison of three-point bending test and peripheral quantitative computed tomography analysis in the evaluation of the strength of mouse femur and tibia. Bone 23:155–161, 1998.

    Article  PubMed  Google Scholar 

  28. Jepsen, K. J., and D. T. Davy. Comparison of damage accumulation measures in human cortical bone. J. Biomech. 30:891–894, 1997.

    Article  CAS  PubMed  Google Scholar 

  29. Katsamanis, F., and D. D. Raftopoulos. Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique. J. Biomech. 23:1173–1184, 1990.

    Article  CAS  PubMed  Google Scholar 

  30. Kaur, M., and K. Singh. Review on titanium and titanium based alloys as biomaterials for orthopaedic applications. Mater. Sci. Eng., C 102:844–862, 2019.

    Article  CAS  Google Scholar 

  31. Keaveny, T. M., E. F. Wachtel, C. M. Ford, and W. Hayes. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J. Biomech. Eng. 27:1137–1146, 1994.

    Article  CAS  Google Scholar 

  32. Kopperdahl, D. L., and T. M. Keaveny. Yield strain behavior of trabecular bone. J. Biomech. Eng. 31:601–608, 1998.

    Article  CAS  Google Scholar 

  33. Kujala, S., J. Ryhänen, T. Jämsä, A. Danilov, J. Saaranen, A. Pramila, and J. Tuukkanen. Bone modeling controlled by a nickel–titanium shape memory alloy intramedullary nail. Biomaterials 23:2535–2543, 2002.

    Article  CAS  PubMed  Google Scholar 

  34. Leppänen, O., H. Sievänen, J. Jokihaara, I. Pajamäki, and T. L. N. Järvinen. Three-point bending of rat femur in the mediolateral direction: introduction and validation of a novel biomechanical testing protocol. J. Bone Miner. Res. 21:1231–1237, 2006.

    Article  PubMed  Google Scholar 

  35. Lessley D., J. Crandall, G. Shaw, R. Kent, and J. Funk. A Normalization Technique for Developing Corridors from Individual Subject Responses. SAE International, 2004.

  36. Lewin, S., I. Fleps, D. Neuhaus, C. Ohman-Magi, S. J. Ferguson, C. Persson, and B. Helgason. Implicit and explicit fi nite element models predict the mechanical response of calcium phosphate-titanium cranial implants. J. Mech. Behav. Biomed. Mater. 112:104085, 2020.

    Article  CAS  PubMed  Google Scholar 

  37. Li, S. M., E. Demirci, and V. V. Silberschmidt. Variability and anisotropy of mechanical behavior of cortical bone in tension and compression. J. Mech. Behav. Biomed. Mater. 21:109–120, 2013.

    Article  PubMed  Google Scholar 

  38. Linde, F., and I. Hvid. Stiffness behaviour of trabecular bone specimens. J. Biomech. 20:83–89, 1987.

    Article  CAS  PubMed  Google Scholar 

  39. Linde, F., and H. C. Sørensen. The effect of different storage methods on the mechanical properties of trabecular bone. J. Biomech. 26:1249–1252, 1993.

    Article  CAS  PubMed  Google Scholar 

  40. McPherson, G. K., and T. J. Kriewall. The elastic modulus of fetal cranial bone: a first step towards an understanding of the biomechanics of fetal head molding. J. Biomech. 13:9–16, 1980.

    Article  CAS  PubMed  Google Scholar 

  41. Mirzaali, M. J., J. J. Schwiedrzik, S. Thaiwichai, J. P. Best, J. Michler, P. K. Zysset, and U. Wolfram. Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly. Bone 93:196–211, 2016.

    Article  PubMed  Google Scholar 

  42. Mo F., H. Zhang, S. Zhao, Z. Xiao, and T. Liu. Coupling musculoskeletal dynamics and subject-specific finite element analysis of femoral cortical bone failure after endoprosthetic knee replacement. Appl. Bionics Biomech. 2019, 2019.

  43. Morgan, E. F., and T. M. Keaveny. Dependence of yield strain of human trabecular bone on anatomic site. J. Biomech. Eng. 34:569–577, 2001.

    Article  CAS  Google Scholar 

  44. Nyman, J. S., H. Leng, X. N. Dong, and X. Wang. Differences in the mechanical behavior of cortical bone between compression and tension when subjected to progressive loading. J. Mech. Behav. Biomed. Mater. 2:613–619, 2009.

    Article  PubMed  Google Scholar 

  45. Ohman, C., E. Dall’Ara, M. Baleani, S. V. S. Jan, and M. Viceconti. The effects of embalming using a 4% formalin solution on the compressive mechanical properties of human cortical bone. Clin. Biomech. 23:1294–1298, 2008.

    Article  Google Scholar 

  46. Ramezanzadehkoldeh, M., and B. H. Skallerud. MicroCT-based finite element models as a tool for virtual testing of cortical bone. Med. Eng. Phys. 46:12–20, 2017.

    Article  PubMed  Google Scholar 

  47. Rho, J.-Y., L. Kuhn-Spearing, and P. Zioupos. Mechanical properties and the hierarchical structure of bone. Med. Eng. Phys. 20:92–102, 1998.

    Article  CAS  PubMed  Google Scholar 

  48. Salim M. S., A. F. Salleh, and R. Daud. Bone fracture modeling and analysis by three point bending: a review. MATEC Web Conf. 77: 2016.

  49. Sedlin, E. D. A rheologic model for cortical bone: a study of the physical properties of human femoral samples. Acta Orthop. Scand. 36:1–77, 1965.

    Article  Google Scholar 

  50. Sharma N., S. Sharma, D. Sehgal, and R. Pandey. Studies on deformational behavior of cortical bone using small punch testing and finite element simulation. Proceedings of the World Congress on Engineering and Computer Science, 2013.

  51. Sharma N. K., S. Sharma, D. K. Sehgal and R. K. Pandey. Detailed analysis of deformation behavior of plexiform bone using small specimen testing and finite element simulation. In: Transactions on Engineering Technologies, Springer, 2014, pp. 661–673.

  52. Tuominen, T., T. Jämsä, J. Tuukkanen, A. Marttinen, T. S. Lindholm, and P. Jalovaara. Bovine bone implant with bovine bone morphogenetic protein in healing a canine ulnar defect. Int. Orthop. 25:5–8, 2001.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Turner, C. H. Bone strength: current concepts. Ann. N. Y. Acad. Sci. 1068:429–446, 2006.

    Article  PubMed  Google Scholar 

  54. Turner, C. H. Yield behavior of bovine cancellous bone. J. Biomech. Eng. 111:256–260, 1989.

    Article  CAS  PubMed  Google Scholar 

  55. Turner, C. H., and D. B. Burr. Basic biomechanical measurements of bone: a tutorial. Bone 14:595–608, 1993.

    Article  CAS  PubMed  Google Scholar 

  56. Turner, C. H., and D. B. Burr. Experimental techniques for bone mechanics. In: Bone Mechanics Handbook, edited by S. C. Cowin. Boca Raton, FL: CPC Press, 2001, pp. 7–20.

    Google Scholar 

  57. Unger, S., M. Blauth, and W. Schmoelz. Effects of three different preservation methods on the mechanical properties of human and bovine cortical bone. Bone 47:1048–1053, 2010.

    Article  PubMed  CAS  Google Scholar 

  58. Untaroiu C., J. Kerrigan and J. Crandall. Material Identification using Successive Response Surface Methodology, with Application to a Human Femur Subjected to Three-Point Bending Loading. SAE International, 2006.

  59. Untaroiu, C. D., and Y. C. Lu. Material characterization of liver parenchyma using specimen-specific finite element models. J. Mech. Behav. Biomed. Mater. 26:11–22, 2013.

    Article  PubMed  Google Scholar 

  60. Untaroiu C. D., W. Pak, Y. Meng, J. Schap, B. Koya, and S. Gayzik. A finite element model of a midsize male for simulating pedestrian accidents. J. Biomech. Eng. 140: 2018.

  61. Untaroiu, C. D., J. Shin, and Y. C. Lu. Assessment of a dummy model in crash simulations using rating methods. Int. J. Autom. Technol. 14:395–405, 2013.

    Article  Google Scholar 

  62. van Haaren E. H., B. C. van der Zwaard, A. J. van der Veen, I. C. Heyligers, P. I. Wuisman and T. H. Smit. Effect of long-term preservation on the mechanical properties of cortical bone in goats. Acta Orthop. 79: 708-716, 2008.

  63. Wallace, J. M., K. Golcuk, M. D. Morris, and D. H. Kohn. Inbred strain-specific response to biglycan deficiency in the cortical bone of C57BL6/129 and C3H/He mice. J. Bone Miner. Res. 24:1002–1012, 2009.

    Article  PubMed  Google Scholar 

  64. Weibull, W. A statistical distribution function of wide applicability. J. Appl. Mech. 18:293–297, 1951.

    Article  Google Scholar 

  65. Weibull, W. A statistical theory of strength of materials. R. Swedish Acad. Eng. Sci. 151:1–45, 1939.

    Google Scholar 

  66. Wieding, J., E. Mick, A. Wree, and R. Bader. Influence of three different preservative techniques on the mechanical properties of the ovine cortical bone. Acta Bioeng. Biomech. 17:137–146, 2015.

    PubMed  Google Scholar 

  67. Wright, T. M., and W. C. Hayes. Tensile testing of bone over a wide range of strain rates: effects of strain rate, microstructure and density. Med. Biol. Eng. 14:671, 1976.

    Article  CAS  PubMed  Google Scholar 

  68. Yang, H. S., X. Ma, and T. T. Guo. Some factors that affect the comparison between isotropic and orthotropic inhomogeneous finite element material models of femur. Med. Eng. Phys. 32:553–560, 2010.

    Article  PubMed  Google Scholar 

  69. Yang, J. F. C., and R. S. Lakes. Experimental study of micropolar and couple stress elasticity in compact bone in bending. J. Biomech. 15:91–98, 1982.

    Article  CAS  PubMed  Google Scholar 

  70. Yeni, Y. N., and D. P. Fyhrie. A rate-dependent microcrack-bridging model that can explain the strain rate dependency of cortical bone apparent yield strength. J. Biomech. 36:1343–1353, 2003.

    Article  PubMed  Google Scholar 

  71. Zhang, G., X. Deng, F. Guan, Z. Bai, L. Cao, and H. Mao. The effect of storage time in saline solution on the material properties of cortical bone tissue. Clin. Biomech. 57:56–66, 2018.

    Article  Google Scholar 

  72. Zhang, G., S. Wang, S. Xu, F. Guan, Z. Bai, and H. Mao. The effect of formalin preservation time and temperature on the material properties of bovine femoral cortical bone tissue. Ann. Biomed. Eng. 47:937–952, 2019.

    Article  PubMed  Google Scholar 

  73. Zhang, G., S. Xu, J. Yang, F. Guan, L. Cao, and H. Mao. Combining specimen-specific finite-element models and optimization in cortical-bone material characterization improves prediction accuracy in three-point bending tests. J. Biomech. 76:103–111, 2018.

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

This research was funded by the National Natural Science Foundation of China (51621004, GZ) and Natural Science Foundation of Hunan Province (2019JJ40034, GZ). We also acknowledge the Canada Research Chairs program (HM).

Conflict of interest

There are no conflicts of interest.

Author information

Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Guanjun Zhang, Junjie Luo, Gang Zheng, Zhonghao Bai & Libo Cao

  2. Department of Mechanical and Materials Engineering, Faculty of Engineering, School of Biomedical Engineering, Western University, London, ON, N6A 5B9, Canada

    Haojie Mao

Authors
  1. Guanjun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junjie Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gang Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhonghao Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Libo Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Haojie Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haojie Mao.

Additional information

Associate Editor Stefan M. Duma oversaw the review of this article.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Below is the link to the electronic supplementary material.

Electronic supplementary material 1 (PDF 2311 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, G., Luo, J., Zheng, G. et al. Is the 0.2%-Strain-Offset Approach Appropriate for Calculating the Yield Stress of Cortical Bone?. Ann Biomed Eng 49, 1747–1760 (2021). https://doi.org/10.1007/s10439-020-02719-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-020-02719-2

Keywords

Search

Navigation