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Medical & Biological Engineering & Computing

, Volume 55, Issue 8, pp 1249–1260 | Cite as

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

  • F. G. A. Silva
  • M. F. S. F. de Moura
  • N. DouradoEmail author
  • J. Xavier
  • F. A. M. Pereira
  • J. J. L. Morais
  • M. I. R. Dias
  • P. J. Lourenço
  • F. M. Judas
Original Article
  • 412 Downloads

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.

Keywords

Bone Fracture characterization Mode II ENF test Cohesive zone modeling 

Notes

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.

References

  1. 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 49:380–389CrossRefPubMedGoogle Scholar
  2. 2.
    Chapra SC (2011) Applied numerical methods with MATLAB® for engineers and scientists. McGraw-Hill EducationGoogle Scholar
  3. 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 33:405–410CrossRefGoogle Scholar
  4. 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):28–47CrossRefGoogle Scholar
  5. 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 51:219–231CrossRefPubMedGoogle Scholar
  6. 6.
    Leffler K, Alfredsson KS, Stigh U (2007) Shear behaviour of adhesive layers. Int J Solids Struct 44:530–545CrossRefGoogle Scholar
  7. 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 3:446–453CrossRefPubMedGoogle Scholar
  8. 8.
    Nalla R, Kinney J, Ritchie R (2003) Mechanistic fracture criteria for the failure of human cortical bone. Nat Mater 2:164–168CrossRefPubMedGoogle Scholar
  9. 9.
    Norman TL, Vashishth D, Burr DB (1995) Fracture toughness of human bone under tension. J Biomech 28:309–320CrossRefPubMedGoogle Scholar
  10. 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 29:1023–1031CrossRefPubMedGoogle Scholar
  11. 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 20:062001CrossRefGoogle Scholar
  12. 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 4:1764–1773CrossRefGoogle Scholar
  13. 13.
    Pope M, Murphy M (1974) Fracture energy of bone in a shear mode. Med Biol Eng Comput 12:763–767CrossRefGoogle Scholar
  14. 14.
    Reinsch C (1967) Smoothing by spline functions. Numer Math 10:177–183Google Scholar
  15. 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 51:54–61CrossRefGoogle Scholar
  16. 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 49:1402–1412CrossRefGoogle Scholar
  17. 17.
    Sousa AMR, Xavier J, Vaz M, Morais JJL, Filipe VMJ (2011) Cross-correlation and differential technique combination to determine displacement fields. Strain 47:87–98CrossRefGoogle Scholar
  18. 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 33:1325–1330CrossRefPubMedGoogle Scholar
  19. 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 26:207–215CrossRefGoogle Scholar
  20. 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 54:829–840Google Scholar
  21. 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 71:109–115CrossRefGoogle Scholar
  22. 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 121:83–89CrossRefGoogle Scholar
  23. 23.
    Yang QD, Cox BN, Nalla RK, Ritchie RO (2006) Fracture length scales in human cortical bone: the necessity of nonlinear fracture models. Biomaterials 27:2095–2113CrossRefPubMedGoogle Scholar
  24. 24.
    Zimmermann EA, Launey ME, Barth HD, Ritchie RO (2009) Mixed-mode fracture of human cortical bone. Biomaterials 30:877–5884CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2016

Authors and Affiliations

  • F. G. A. Silva
    • 1
  • M. F. S. F. de Moura
    • 2
  • N. Dourado
    • 3
    Email author
  • J. Xavier
    • 1
    • 4
  • F. A. M. Pereira
    • 2
    • 4
  • J. J. L. Morais
    • 4
  • M. I. R. Dias
    • 4
  • P. J. Lourenço
    • 5
  • F. M. Judas
    • 5
  1. 1.INEGI - Instituto de Ciência e Inovação em Engenharia Mecânica e Engenharia IndustrialPortoPortugal
  2. 2.Departamento de Engenharia MecânicaFaculdade de Engenharia da Universidade do PortoPortoPortugal
  3. 3.CMEMS-UMinho, Departamento de Engenharia MecânicaUniversidade do MinhoGuimarãesPortugal
  4. 4.Centre for the Research and Technology of Agro-Environmental and Biological Sciences, CITABUniversity of Trás-os-Montes and Alto Douro, UTADVila RealPortugal
  5. 5.Banco de Tecidos Ósseos do Centro Hospitalar e Universitário de Coimbra - CHUC, EPEFaculdade de Medicina da Universidade de CoimbraCoimbraPortugal

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