Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoind
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J.G. Swadener Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received 23 May 2003; accepted 16 September 2003)
A three-dimensional finite element analysis (FEA) model with elastic–plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver–Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver–Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy. I. INTRODUCTION
Nanoindentation is widely used in the materialsscience community for probing the mechanical properties of thin films, small volumes, and small microstructural features.1 Due to its convenience of specimen preparation and ability of elastic property measurement, nanoindentation tests have been applied to the measurement of bone mechanical properties.2–7 As shown in Fig. 1, cortical bone has an obvious hierarchical structure that gives bone a capability to perform diverse mechanical, biological, and chemical functions, such as structural support, protection and storage of healing cells, and mineral ion homeostasis. Osteonic lamella is the most distinguishable component at the microstructural level. It plays an important role in determining bone mechanical properties. However, because the available mechanical testing method at the submicrostructural level is limited, mechanical properties of individual lamellae are rarely found in the literature. It has been shown that nanoindentation could be used to quantitatively reveal
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Address all correspondence to this author. Present address: Zaifeng Fan, Orthopedic & Rehabilitation Engineering Center, Marquette University, Academic Support Facility 105, 735 N. 17th St., P.O. Box 1881, Milwaukee, WI 53201-1881. e-mail: [email protected]
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J. Mater. Res., Vol. 19, No. 1, Jan 2004
the anisotropy of cortical bone at the microstructural level.8,9 It was found that the indentation moduli exhibited varied values when indent orientations varied. Because nanoindentation analysis is developed based on isotropic material properties, the test result from bone material is actually a mixed value. The indentation modulus is 1–10% larger than the Young’s modulus (depending on Poisson’s ratio) in most isotropic materials, whereas the indentation modulus may differ greatly from the Young’s modu
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