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Acta Bioeng Biomech. 2015;17(2):3-14.

A numerical study on indentation properties of cortical bone tissue: influence of anisotropy.

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Department of Mechanical Engineering, University of Turkish Aeronautical Association, 06790 Ankara, Turkey.
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, LE11 3TU, UK.



The purpose of this study is to investigate the effect of anisotropy of cortical bone tissue on measurement of properties such as direction-dependent moduli and hardness.


An advanced three-dimensional finite element model of microindentation was developed. Different modelling schemes were considered to account for anisotropy of elastic or/and plastic regimes. The elastic anisotropic behaviour was modelled employing an elasticity tensor, and Hill's criteria were used to represent the direction-dependent post-yield behaviour. The Oliver-Pharr method was used in the data analysis.


A decrease in the value of the transverse elasticity modulus resulted in the increased material's indentation modulus measured in the longitudinal direction and a decreased one in the transverse direction, while they were insensitive to the anisotropy in post-elastic regime. On the other hand, an increase in plastic anisotropy led to a decrease in measured hardness for both directions, but by a larger amount in the transverse one. The size effect phenomenon was found to be also sensitive to anisotropy.


The undertaken analysis suggests that the Oliver-Pharr method is a useful tool for first-order approximations in the analysis of mechanical properties of anisotropic materials similar to cortical bone, but not necessarily for the materials with low hardening reserves in the plastic regime.

[Indexed for MEDLINE]

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