Keywords: trabecular bone, nanoindentation, computed tomography, apparent modulus.

The paper shows the possibility of using microstructural finite element (FE) models of trabecular bone to model its failure behavior. The behavior of trabecular microstructure under uniaxial compression and tension is studied and the response of the FE models compared to experimentally determined stress-strain diagrams. The importance of proper segmentation of the bone tissue from CT-images, the quality of the tetrahedral elements, as well as the need for using quadratic shape functions are underlined in the paper. The choice of proper yield criteria, the need for anisotropic plasticity and large deformation analysis are also discussed as well.

The most common criterion used to study the failure behavior of trabecular bone is the von Mises criterion [1,2]. However, trabecular bone possess very distinct yield strains in compression and tension. Therefore, it is essential to apply anisotropic plasticity for the failure analysis of trabecular bone. The only publication which uses high-resolution FE model of trabecular bone and refers to the phenomena is the work of Niebur et al. [3]. Up to now, comparison of different plasticity criteria applied to the failure analysis of trabecular bone has not been published.

The response of the FE model is compared to apparent material properties obtained experimentally using a special loading device. In conclusion, the adopted procedures are found to be a robust and precise method to predict the material properties of trabecular bone; provided that the trabecular bone structure is segmented properly from the tomographic images. The procedures described are promising for detailed analysis of the deformation behavior of materials with a complex inner structure, e.g. trabecular bone.

The results obtained by FE modeling indicate a great importance of the quality of tetrahedral elements, the need for second-order elements and the proper surface detection when converting the µCT data into a surface mesh. In both voxel and tetrahedral meshes the strain distribution is very localized imposing special requirements on the mesh quality. Considering anisotropic plasticity with kinematic hardening is of great importance even for small strains.

1

Nagaraja S., Couse T.L., Guldberg R.E., "Trabecular bone microdamage and microstructural stresses under uniaxial compression", Journal of Biomechanics, 38(4), 707-716, April 2005. doi:10.1016/j.jbiomech.2004.05.013

2

Ulrich D., van Rietbergen B., Weinans H., Rüegsegger P., "Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques", Journal of Biomechanics, 31(12), 1187-1192, 1998. doi:10.1016/S0021-9290(98)00118-3

3

Niebur G.L., Feldstein M.J., Yuen J.C., Chen T.J., Keaveny T.M., "High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone", Journal of Biomechanics, 33(12), 1575-1583, December 2000. doi:10.1016/S0021-9290(00)00149-4

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