An Alternative Fabric-based Yield and Failure Criterion for Trabecular Bone

  • Ph. Zysset
  • L. Rincón

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arcan, M., Hashin, Z., and Voloshin, A. (1978). A method to produce uniform plane-stress states with applications to fiber-reinforced materials. Exp. Mech. 18:141–146.CrossRefGoogle Scholar
  2. Arramon, Y. P., Mehrabadi, M. M., Martin, D. W., and Cowin, S. C. (2000). A multidimensional anisotropic strength criterion based on kelvin modes. Int. J. Solids Structures 37:2915–2935.CrossRefMATHGoogle Scholar
  3. Boehler, J. P., ed. (1987). Applications of Tensor Functions in Solid Mechanics. Wien: Springer-Verlag. CISM Courses and Lectures No. 292, International Centre for Mechanical Sciences.MATHGoogle Scholar
  4. Chang, W. C. W., Christensen, T. M., Pinilla, T. P., and Keaveny, T. M. (1999). Isotropy of uniaxial yield strains for bovine trabecular bone. J. Orthop. Res. 17:582–585.CrossRefGoogle Scholar
  5. Cowin, S. C., and He, Q.-C. (2005). Tensile and compressive stress yield criteria for cancellous bone. J. Biomech. 38:141–144.Google Scholar
  6. Cowin, S. C., and Van Buskirk, W. C. (1986). Thermodynamic restriction of the elastic constants of bone. J. Biomech. 19:85–87.CrossRefGoogle Scholar
  7. Cowin, S. C. (1985). The relationship between the elasticity tensor and the fabric tensor. Mech. Mat. 4:137–147.CrossRefGoogle Scholar
  8. Curnier, A., He, Q.-C., and Zysset, P. (1995). Conewise linear elastic materials. J. Elasticity 37:1–38.MathSciNetCrossRefMATHGoogle Scholar
  9. Deshpande, V. S., and Fleck, N. A. (2000). Isotropic constitutive model for metallic foams. J. Mech. Phys. Solids 48:1253–1283.CrossRefMATHGoogle Scholar
  10. Fenech, C. M., and Keaveny, T. M. (1999). A cellular solid criterion for predicting the axial-shear failure properties of bovine trabecular bone. J. Biomech. Eng. 121:414–422.Google Scholar
  11. Gibson, L. J., and Ashby, M. F. (1988). Cellular solids. Oxford: Pergamon Press.MATHGoogle Scholar
  12. Gioux, G., McCormack, T. M., and Gibson, L. J. (2000). Failure of aluminium foams under multiaxial loads. Int. J. Mech. Sci. 42:1097–1117.CrossRefMATHGoogle Scholar
  13. Goulet, R. W., Goldstein, S. A., Ciarelli, M. J., Kuhn, J. L., Brown, M. B., and Feldkamp, L. A. (1994). The relationship between the structural and orthogonal compressive properties of trabecular bone. J. Biomech. 27: 375–389.CrossRefGoogle Scholar
  14. Harrigan, T. P., and Mann, R. W. (1984). Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mat. Sci. 19:761–767.CrossRefGoogle Scholar
  15. Hoffman, O. (1967). The brittle strength of orthotropic materials. J. Compos. Mater. 1:200–206.Google Scholar
  16. Kanatani, K.-I. (1984). Distribution of directional data and fabric tensors. Int. J. Eng. Sci. 22:149–164.MATHMathSciNetCrossRefGoogle Scholar
  17. Keaveny, T. M., Wachtel, E. F., Ford, C. M., and Hayes, W. C. (1994a). Differences between the tensile and compressive strength of bovine tibial trabecular bone depend on modulus. J. Biomech. 27:1137–1146.CrossRefGoogle Scholar
  18. Keaveny, T. M., Wachtel, E. F., Guo, X. E., and Hayes, W. C. (1994b). Mechanical behavior of damaged trabecular bone. J. Biomech. 27:1309–1318.CrossRefGoogle Scholar
  19. Keaveny, T. M., Wachtel, E. F., Zadesky, S. P., and Arramon, Y. P. (1999). Application of the tsai-wu quadratic multiaxial failure criterion to bovine trabecular bone. J. Biomech. Eng. 121:99–107.Google Scholar
  20. Kopperdahl, D. L., and Keaveny, T. M. (1998). Yield strain behavior of trabecular bone. J. Biomech. 31:601–608.CrossRefGoogle Scholar
  21. Miller, R. E. (2000). A continuum plasticity model for the constitutive and indentation behaviour of foamed metals. Int. J. Mech. Sci. 42:729–754.MATHCrossRefGoogle Scholar
  22. Morgan, E. F., Arramon, Y. P., Kopperdahl, D. L., and Keaveny, T. M. (1999). Dependence of yield strain on anatomic site for human trabecular bone. In Bioengineering Conference. The American Society of Mechanical Engineers (ASME). BED-Vol. 43, 23–24.Google Scholar
  23. Pietruszak, S., Inglis, D., and Pande, G. N. (1999). A fabric-dependent fracture criterion for bone. J. Biomech. 32:1071–1079.CrossRefGoogle Scholar
  24. Rice, J. C., Cowin, S. C., and Bowman, J. A. (1988). On the dependence of the elasticity and strength of cancellous bone on apparent density. J. Biomech. 21:155–168.CrossRefGoogle Scholar
  25. Rincon-Kohli, L. (2003). Identification of a multiaxial failure criterion for human trabecular bone. Ph.D. Dissertation, Swiss Federal Institute of Technology, Lausanne.Google Scholar
  26. Stone, J. L., Beaupre, G. S., and Hayes, W. C. (1983). Multiaxial strength characteristics of trabecular bone. J. Biomech. 16:743–752.CrossRefGoogle Scholar
  27. Tsai, S. W., and Wu, E. M. (1971). A general theory of strength of anisotropic materials. J. Compos. Mater. 5:58–80.Google Scholar
  28. Turner, C. H., Rho, J., Takano, Y., Tsui, T. Y., and Pharr, G. M. (1999). The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J. Biomech. 32:437–441.CrossRefGoogle Scholar
  29. Turner, C. H. (1989). Yield behavior of bovine cancellous bone. J. Biomech. Eng. 111:256–260.CrossRefGoogle Scholar
  30. Zysset, P. K., and Curnier, A. (1995). An alternative model for anisotropic elasticity based on fabric tensors. Mech. Mat. 21:243–250.CrossRefGoogle Scholar
  31. Zysset, P. (2003). A review of fabric-elasticity relationships for human trabecular bone: theories and experiments. J. Biomech. 36:1469–1485.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ph. Zysset
    • 1
  • L. Rincón
    • 2
  1. 1.Institute for Lightweight Design and Structural BiomechanicsTU-WienAustria
  2. 2.Stryker TraumaSwitzerland

Personalised recommendations