ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

The difference in pile-up between friction coefficients of 0.3 and 0.0 respectively for the
3D model is presented in Figure 5.
(a) (b)
Fig. 5: A top-view (X-Z plane) of pile-up height variation (in µm) for the 3D simulations with
indenter-bone coefficient of friction (a) µ = 0.3 and (b) µ = 0.0 (frictionless).
5. DISCUSSION
The purpose of this study was to compare the predicted behaviour of a 2D axisymmetric
FE model with a 3D model of the high-load nanoindentation of bone tissue using a
Berkovich indenter. This investigation was undertaken to understand whether the
previously noted ability of 2D axisymmetric models to represent Berkovich indenters
accurately with respect to the force-displacement response of thin films [7] also
extended to the prediction of pile-up around the indenter.
The minimal variation of the force-displacement curves found in this study between 2D
and 3D models with different friction coefficients is consistent with existing literature
[6, 7]. However, differences in pile-up height of up to 40% were observed between the
2D and 3D simulations. Using 2D axisymmetric simulation to predict pile-up may
therefore significantly underestimate the pile-up generated around the Berkovich tip and
thus adversely affect constitutive model decisions and parameter selection. What is lost
in computational expense with 3D models may be gained by learning more about the
plastic response of bone tissue.
We note that the von Mises material model used in this study has been recently proven
to be unable to accurately predict the plastic behaviour of cortical bone tissue [4].
However it was used as a starting point in this study for consistency with the work of
previous authors [4,6] and also because the incompressible plastic flow which occurs in
von Mises plasticity may be appropriate for modelling the pile-up which we have
recently observed under high-load indentation conditions (unpublished data).
The value of friction assumed between the indenter and bone surface has been shown to
play a role in the predicted pile-up height [6]. This previous work was extended in the