A finite element model was developed for numerical simulations of nanoindentation tests on cortical bone. The model allows for anisotropic elastic and post-yield behavior of the tissue. The material model for the post-yield behavior was obtained through a suitable linear transformation of the stress tensor components to define the properties of the real anisotropic material in terms of a fictitious isotropic solid. A tension-compression yield stress mismatch and a direction-dependent yield stress are allowed for. The constitutive parameters are determined on the basis of literature experimental data. Indentation experiments along the axial (the longitudinal direction of long bones) and transverse directions have been simulated with the purpose to calculate the indentation moduli and the tissue hardness in both the indentation directions. The results have shown that the transverse to axial mismatch of indentation moduli was correctly simulated regardless of the constitutive parameters used to describe the post-yield behavior. The axial to transverse hardness mismatch observed in experimental studies (see, for example, Rho et al. [1999, “Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation,” J. Biomed. Mater. Res., 45, pp. 48–54] for results on human tibial cortical bone) can be correctly simulated through an anisotropic yield constitutive model. Furthermore, previous experimental results have shown that cortical bone tissue subject to nanoindentation does not exhibit piling-up. The numerical model presented in this paper shows that the probe tip-tissue friction and the post-yield deformation modes play a relevant role in this respect; in particular, a small dilatation angle, ruling the volumetric inelastic strain, is required to approach the experimental findings.
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August 2010
Research Papers
A Finite Element Model for Direction-Dependent Mechanical Response to Nanoindentation of Cortical Bone Allowing for Anisotropic Post-Yield Behavior of the Tissue
D. Carnelli,
D. Carnelli
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy; Department of Materials Science and Engineering, Massachusetts Institute of Technology
, Cambridge, MA 02139
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D. Gastaldi,
D. Gastaldi
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy
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V. Sassi,
V. Sassi
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy
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R. Contro,
R. Contro
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy
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C. Ortiz,
C. Ortiz
Department of Materials Science and Engineering,
Massachusetts Institute of Technology
, Cambridge, MA 02139
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P. Vena
P. Vena
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
e-mail: vena@stru.polimi.it
Politecnico di Milano
, 20133 Italy; IRCCS, Istituto Ortopedico Galeazzi
, Milano, 20161 Italy
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D. Carnelli
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy; Department of Materials Science and Engineering, Massachusetts Institute of Technology
, Cambridge, MA 02139
D. Gastaldi
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy
V. Sassi
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy
R. Contro
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy
C. Ortiz
Department of Materials Science and Engineering,
Massachusetts Institute of Technology
, Cambridge, MA 02139
P. Vena
Department of Structural Engineering, Laboratory of Biological Structure Mechanics (LaBS),
Politecnico di Milano
, 20133 Italy; IRCCS, Istituto Ortopedico Galeazzi
, Milano, 20161 Italye-mail: vena@stru.polimi.it
J Biomech Eng. Aug 2010, 132(8): 081008 (10 pages)
Published Online: June 18, 2010
Article history
Received:
July 20, 2009
Revised:
February 18, 2010
Posted:
March 1, 2010
Published:
June 18, 2010
Online:
June 18, 2010
Citation
Carnelli, D., Gastaldi, D., Sassi, V., Contro, R., Ortiz, C., and Vena, P. (June 18, 2010). "A Finite Element Model for Direction-Dependent Mechanical Response to Nanoindentation of Cortical Bone Allowing for Anisotropic Post-Yield Behavior of the Tissue." ASME. J Biomech Eng. August 2010; 132(8): 081008. https://doi.org/10.1115/1.4001358
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