Skip to main content
Log in

Experimental and analytical study of anisotropic strength properties of bovine cortical bone

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

This paper is focused on specification of conditions at failure in bovine cortical bone. Both experimental and analytical studies are conducted. The experimental part includes a series of novel direct shear tests which examine the sensitivity of shear strength to the applied normal stress for different orientations of the sample microstructure. These experiments are supplemented by standard axial compression and tension tests in order to define and quantify a general form of failure criterion. The analytical part examines two different methodologies, viz. critical plane approach and microstructure tensor approach, for defining the anisotropic strength criterion. A procedure for identification of material parameters is outlined which is based on the results of the performed material tests.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Boehler JP, Sawczuk A (1977) On yielding of oriented solids. Acta Mech 27:185–206

    Article  Google Scholar 

  • Cowin SC (1979) On the strength anlsotropy of bone and wood. J Appl Mech 46:832–838

    Article  Google Scholar 

  • Cowin SC (1986) Fabric dependence of an anisotropic strength criterion. Mech Mater 5:251–260

    Article  Google Scholar 

  • Cowin SC (1999) Bone poroelasticity. J Biomech 32:217–238

    Article  Google Scholar 

  • Das BM (2002) Soil mechanics laboratory manual, 6th edn. Oxford University Press, New York

    Google Scholar 

  • Dong XN, Luo Q, Wang X (2013) Progressive post-yield behavior of human cortical bone in shear. Bone 53(1):1–5. https://doi.org/10.1016/j.bone.2012.11.029

    Article  Google Scholar 

  • Fenech CM, Keaveny TM (1999) A cellular solid criterion for predicting the axial-shear failure properties of bovine trabecular bone. J Biomech Eng 121:414–422

    Article  Google Scholar 

  • Gao H et al (2003) Materials become insensitive to flaws at nanoscale: lessons from nature. Proc Natl Acad Sci U S A 100(10):5597–5600

    Article  Google Scholar 

  • Garcia D, Zysset PK, Charlebois M, Curnier A (2009) A three-dimensional elastic plastic damage constitutive law for bone tissue. Biomech Model Mechanobiol 8:149–165

    Article  Google Scholar 

  • Hayes WC, Wright TM (1977) An empiricl strength theory for compact bone. Fracture 3:1173–1179

    Google Scholar 

  • Hill R (1950) The mathematical theory of plasticity. Oxford University Press, London

    MATH  Google Scholar 

  • Jäger I, Fratzl P (2000) Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys J 79(4):1737–1746

    Article  Google Scholar 

  • Keaveny TM et al (1997) Systematic and random errors in compression testing of trabecular bone. J Orthop Res 15(1):101–110

    Article  Google Scholar 

  • Martin RB, Burr DB, Sharkey NA, Fyhrie DP (2016) Skeletal tissue mechanics, 2nd edn. Springer, New York

    Google Scholar 

  • Niebur GL et al (2000) High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular Bone. J Biomech 33:1575–1583

    Article  Google Scholar 

  • Nyman JS, Leng H, Dong XN, Wang X (2009) Differences in the mechanical behavior of cortical bone between compression and tension when subjected to progressive loading. J Mech Behav Biomed Mater 2(6):613–619. https://doi.org/10.1016/j.jmbbm.2008.11.008

    Article  Google Scholar 

  • Odgaard A, Linde F (1991) The underestimation of Young’s modulus in compressive testing of cancellous bone specimens. J Biomech 24(8):691–698

    Article  Google Scholar 

  • Park HC, Lakes RS (1986) Cosserat micromechanics of human bone: strain redistribution by a hydration sensitive constituent. J Biomech Eng 19(5):385–397

    Article  Google Scholar 

  • Piekarski K (1973) Analysis of bone as a composite material. Int J Eng Sci 11(6):557–565

    Article  Google Scholar 

  • Pietruszczak S (2010) Fundamentals of plasticity in geomechanics. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Pietruszczak S, Gdela K (2010) Inelastic analysis of fracture propagation in distal radius. J Appl Mech 77:1–10

    Article  Google Scholar 

  • Pietruszczak S, Mroz Z (2001) On failure criteria for anisotropic cohesive-frictional materials. Int J Numer Anal Meth Geomech 25(5):509–524

    Article  Google Scholar 

  • Pietruszczak S, Inglis D, Pande GN (1999) A fabric-dependent fracture criterion for bone. J Biomech 32(10):1071–1079

    Article  Google Scholar 

  • Pistoia W et al (2002) Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images. Bone 30(6):842–848

    Article  Google Scholar 

  • Reilly DT, Burstein AH (1975) The elastic and ultimate properties of compact bone tissue. J Biomech 8(6):393–405

    Article  Google Scholar 

  • Rincón-Kohli L, Zysset PK (2009) Multi-axial mechanical properties of human trabecular bone. Biomech Model Mechanobiol 8(3):195–208

    Article  Google Scholar 

  • Saha S (1977) Longitudinal shear properties of human compact bone and its constituents, and the associated failure mechanisms. J Material Sci 12:1798–1806

    Article  Google Scholar 

  • Tsai SW, Wu EM (1971) A general theory of strength for anisotropic materials. J Compos Mater 5(1):58–80

    Article  Google Scholar 

  • Turner CH, Wang T, Burr DB (2001) Shear strength and fatigue properties of human cortical bone determined from pure shear tests. Calcif Tissue Int 69:373–378

    Article  Google Scholar 

  • Ulrich D, Rietbergen BV, Laib A, Rüegsegger P (1999) Load transfer analysis of the distal radius from in-vivo high resolution CT imaging. J Biomech 32:821–828

    Article  Google Scholar 

  • Winwood K et al (2006) Strain patterns during tensile, compressive, and shear fatigue of human cortical bone and implications for bone biomechanics. J Biomed Mater Res 79(2):289–297

    Article  Google Scholar 

  • Zdero R (2017) Experimental methods in orthopaedic biomechanics. Academic Press, London

    Google Scholar 

  • Zioupos P, Gresle M, Winwood K (2007) Fatigue strength of human cortical bone: age, physical, and material heterogeneity effects. J Biomed Mater Res 86:627–636

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Pietruszczak.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohammadi, H., Pietruszczak, S. Experimental and analytical study of anisotropic strength properties of bovine cortical bone. Biomech Model Mechanobiol 19, 1953–1963 (2020). https://doi.org/10.1007/s10237-020-01319-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-020-01319-2

Keywords

Navigation