The identification of anisotropic elastic properties of lamellar bone based on nanoindentation data is an open problem. Therefore, the purpose of this study was to develop a method to estimate the orthotropic elastic constants of human cortical bone secondary osteons using nanoindentation in two orthogonal directions. Since the indentation modulus depends on all elastic constants and, for anisotropic materials, also on the indentation direction, a theoretical model quantifying the indentation modulus from the stiffness tensor of a given material was implemented numerically (Swadener and Pharr, 2001, “Indentation of Elastically Anisotropic Half-Spaces by Cones and Parabolae of Revolution,” Philos. Mag. A, 81(2), pp. 447–466). Nanoindentation was performed on 22 osteons of the distal femoral shaft: A new holding system was designed in order to indent the same osteon in two orthogonal directions. To interpret the experimental results and identify orthotropic elastic constants, an inverse procedure was developed by using a fabric-based elastic model for lamellar bone. The experimental indentation moduli were found to vary with the indentation direction and showed a marked anisotropy. The estimated elastic constants showed different degrees of anisotropy among secondary osteons of the same bone and these degrees of anisotropy were also found to be different than the one of cortical bone at the macroscopic level. Using the log-Euclidean norm, the relative distance between the compliance tensors of the estimated mean osteon and of cortical bone at the macroscopic level was 9.69%: Secondary osteons appeared stiffer in their axial and circumferential material directions, and with a greater bulk modulus than cortical bone, which is attributed to the absence of vascular porosity in osteonal properties. The proposed method is suitable for identification of elastic constants from nanoindentation experiments and could be adapted to other (bio)materials, for which it is possible to describe elastic properties using a fabric-based model.
Skip Nav Destination
e-mail: giampaolo.franzoso@polimi.it
e-mail: philippe.zysset@ilsb.tuwien.ac.at
Article navigation
February 2009
Research Papers
Elastic Anisotropy of Human Cortical Bone Secondary Osteons Measured by Nanoindentation
Giampaolo Franzoso,
Giampaolo Franzoso
Laboratory of Biological Structure Mechanics (LaBS), Structural Engineering Department,
e-mail: giampaolo.franzoso@polimi.it
Politecnico di Milano
, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
Search for other works by this author on:
Philippe K. Zysset
Philippe K. Zysset
Institute of Lightweight Design and Structural Biomechanics (ILSB),
e-mail: philippe.zysset@ilsb.tuwien.ac.at
Vienna University of Technology
, Gußhausstraße 27-29, A-1040 Vienna, Austria
Search for other works by this author on:
Giampaolo Franzoso
Laboratory of Biological Structure Mechanics (LaBS), Structural Engineering Department,
Politecnico di Milano
, Piazza Leonardo da Vinci 32, 20133 Milano, Italye-mail: giampaolo.franzoso@polimi.it
Philippe K. Zysset
Institute of Lightweight Design and Structural Biomechanics (ILSB),
Vienna University of Technology
, Gußhausstraße 27-29, A-1040 Vienna, Austriae-mail: philippe.zysset@ilsb.tuwien.ac.at
J Biomech Eng. Feb 2009, 131(2): 021001 (11 pages)
Published Online: December 9, 2008
Article history
Received:
December 14, 2007
Revised:
September 20, 2008
Published:
December 9, 2008
Citation
Franzoso, G., and Zysset, P. K. (December 9, 2008). "Elastic Anisotropy of Human Cortical Bone Secondary Osteons Measured by Nanoindentation." ASME. J Biomech Eng. February 2009; 131(2): 021001. https://doi.org/10.1115/1.3005162
Download citation file:
Get Email Alerts
Estimation of Joint Kinetics During Manual Material Handling Using Inertial Motion Capture: A Follow-Up Study
J Biomech Eng (February 2025)
Effect of Compressive Strain Rates on Viscoelasticity and Water Content in Intact Porcine Stomach Wall Tissues
J Biomech Eng (February 2025)
Eyelid Motion Tracking During Blinking Using High-Speed Imaging and Digital Image Correlation
J Biomech Eng (January 2025)
Related Articles
Linear Poroelastic Cancellous Bone Anisotropy: Trabecular Solid Elastic and Fluid Transport Properties
J Biomech Eng (October,2002)
A Model for Prediction of Bone Stiffness Using a Mechanical Approach of Composite Materials
J Biomech Eng (August,2007)
Finite Element Prediction of Proximal Femoral Fracture Patterns Under Different Loads
J Biomech Eng (February,2005)
Quantifying the Anisotropy in Biological Materials
J. Appl. Mech (November,2011)
Related Proceedings Papers
Related Chapters
Novel and Efficient Mathematical and Computational Methods for the Analysis and Architecting of Ultralight Cellular Materials and their Macrostructural Responses
Advances in Computers and Information in Engineering Research, Volume 2
Effect of Temperature and Irradiation on the Hardness of δ-Zr Hydride
Zirconium in the Nuclear Industry: 20th International Symposium
Mathematical Background
Vibrations of Linear Piezostructures