Skip to main content
Log in

Fracture characterization of human cortical bone under mode II loading using the end-notched flexure test

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

Fracture characterization of human cortical bone under mode II loading was analyzed using a miniaturized version of the end-notched flexure test. A data reduction scheme based on crack equivalent concept was employed to overcome uncertainties on crack length monitoring during the test. The crack tip shear displacement was experimentally measured using digital image correlation technique to determine the cohesive law that mimics bone fracture behavior under mode II loading. The developed procedure was validated by finite element analysis using cohesive zone modeling considering a trapezoidal with bilinear softening relationship. Experimental load-displacement curves, resistance curves and crack tip shear displacement versus applied displacement were used to validate the numerical procedure. The excellent agreement observed between the numerical and experimental results reveals the appropriateness of the proposed test and procedure to characterize human cortical bone fracture under mode II loading. The proposed methodology can be viewed as a novel valuable tool to be used in parametric and methodical clinical studies regarding features (e.g., age, diseases, drugs) influencing bone shear fracture under mode II loading.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Brown CU, Yeni YN, Norman TL (2000) Fracture toughness is dependent on bone location—a study of the femoral neck, femoral shaft, and the tibial shaft. J Biomed Mater Res 49:380–389

    Article  CAS  PubMed  Google Scholar 

  2. Chapra SC (2011) Applied numerical methods with MATLAB® for engineers and scientists. McGraw-Hill Education

  3. Dourado N, Pereira FAM, de Moura MFSF, Morais JJL, Dias MIR (2013) Bone fracture characterization using the end notched flexure test. Mat Sci Eng C Mater 33:405–410

    Article  CAS  Google Scholar 

  4. Gonçalves JPM, de Moura MFSF, de Castro PMST, Marques AT (2000) Interface element including point-to-surface constraints for three-dimensional problems with damage propagation. Eng Comput 17(1):28–47

    Article  Google Scholar 

  5. Hambli R (2013) A quasi-brittle continuum damage finite element model of the human proximal femur based on element deletion. Med Biol Eng Comput 51:219–231

    Article  PubMed  Google Scholar 

  6. Leffler K, Alfredsson KS, Stigh U (2007) Shear behaviour of adhesive layers. Int J Solids Struct 44:530–545

    Article  Google Scholar 

  7. Morais JJL, de Moura MFSF, Pereira FAM, Xavier J, Dourado N, Dias MIR, Azevedo JMT (2010) The double cantilever beam test applied to mode I fracture characterization of cortical bone tissue. J Mech Behav Biomed Mater 3:446–453

    Article  CAS  PubMed  Google Scholar 

  8. Nalla R, Kinney J, Ritchie R (2003) Mechanistic fracture criteria for the failure of human cortical bone. Nat Mater 2:164–168

    Article  CAS  PubMed  Google Scholar 

  9. Norman TL, Vashishth D, Burr DB (1995) Fracture toughness of human bone under tension. J Biomech 28:309–320

    Article  CAS  PubMed  Google Scholar 

  10. Norman TL, Nivargikar V, Burr DB (1996) Resistance to crack growth in human cortical bone is greater in shear than in tension. J Biomech 29:1023–1031

    Article  CAS  PubMed  Google Scholar 

  11. Pan B, Qian K, Xie H, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20:062001

    Article  Google Scholar 

  12. Pereira FAM, Morais JJL, Dourado N, de Moura MFSF, Dias MIR (2011) Fracture characterization of bone under mode II loading using the end loaded split test. J Mech Behav Biomed 4:1764–1773

    Article  CAS  Google Scholar 

  13. Pope M, Murphy M (1974) Fracture energy of bone in a shear mode. Med Biol Eng Comput 12:763–767

    Article  CAS  Google Scholar 

  14. Reinsch C (1967) Smoothing by spline functions. Numer Math 10:177–183

    Google Scholar 

  15. Silva F, Morais J, Dourado N, Xavier J, Pereira FAM, de Moura MFSF (2014) Determination of cohesive laws in wood bonded joints under mode II loading using the ENF test. Int J Adhes Adhes 51:54–61

    Article  CAS  Google Scholar 

  16. Sousa AMR, Xavier J, Morais JJL, Filipe VMJ, Vaz M (2011) Processing discontinuous displacement fields by a spatio-temporal derivative technique. Opt Laser Eng 49:1402–1412

    Article  Google Scholar 

  17. Sousa AMR, Xavier J, Vaz M, Morais JJL, Filipe VMJ (2011) Cross-correlation and differential technique combination to determine displacement fields. Strain 47:87–98

    Article  Google Scholar 

  18. Wirtz DC, Schiffers N, Pandorf T, Radermacher K, Weichert D, Forst R (2000) Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. J Biomech 33:1325–1330

    Article  CAS  PubMed  Google Scholar 

  19. Xavier J, de Jesus AMP, Morais JJL, Pinto JMT (2012) Stereovision measurements on evaluating the modulus of elasticity of wood by compression tests parallel to the grain. Constr Build Mater 26:207–215

    Article  Google Scholar 

  20. Xavier J, Oliveira J, Monteiro P, Morais JJL, de Moura MFSF (2014) Direct evaluation of cohesive law in mode I of Pinus pinaster by digital image correlation. Exp Mech 54:829–840

    Google Scholar 

  21. Xavier J, Oliveira M, Morais J, de Moura MFSF (2014) Determining mode II cohesive law of Pinus pinaster by combining the end-notched flexure test with digital image correlation. Constr Build Mater 71:109–115

    Article  Google Scholar 

  22. Xavier J, Fernandes JRA, Frazão O, Morais JJL (2015) Measuring mode I cohesive law of wood bonded joints by combining digital image correlation and fibre Bragg grating sensors. Compos Struct 121:83–89

    Article  Google Scholar 

  23. Yang QD, Cox BN, Nalla RK, Ritchie RO (2006) Fracture length scales in human cortical bone: the necessity of nonlinear fracture models. Biomaterials 27:2095–2113

    Article  CAS  PubMed  Google Scholar 

  24. Zimmermann EA, Launey ME, Barth HD, Ritchie RO (2009) Mixed-mode fracture of human cortical bone. Biomaterials 30:877–5884

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the Portuguese Foundation for Science and Technology (FCT) for the conceded financial support through the research project PTDC/EME-PME/119093/2010.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Dourado.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Silva, F.G.A., de Moura, M.F.S.F., Dourado, N. et al. Fracture characterization of human cortical bone under mode II loading using the end-notched flexure test. Med Biol Eng Comput 55, 1249–1260 (2017). https://doi.org/10.1007/s11517-016-1586-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-016-1586-6

Keywords

Navigation