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

(a) (b)
Fig. 1: (a) 2D axisymmetric and (b) 3D mesh with refinement in region of tip contact and pile-up.
3.2 Material model
All simulations assumed isotropic linear elasticity with elastic modulus E = 13.56 GPa
and Poisson’s ratio υ = 0.3. Plasticity was incorporated using an elastic-perfectly plastic
material model with von Mises yield surface and effective yield stress σyield = 301 MPa.
These values were based on the work of Mullins et al. [4].
3.3 Loads and boundary conditions
Two load steps were used to model the indentation experiment. Firstly a downward
displacement of the indenter by 2.55 µm and secondly an unloading step to return the
indenter to its original position. All other degrees of freedom of the indenter were
constrained. This indentation depth corresponds to high-load nanoindentation and was
based on preliminary experiments in our laboratory indicating that pile-up of bone tissue
can be observed by atomic force microscopy at indentation depths of this magnitude
(unpublished data). During the simulations, the bottom surface of each model was fully
constrained. The vertical axis below the tip was permitted motion only in the Ydirection
(see Figure 1) and each radial face of the cylinder was constrained within its
original plane. Following Adam et al. [6], friction was included in the simulation
through a penalty algorithm with ‘hard’ contact normal to the contact surfaces. In this
manner, the frictional coefficient between the indenter and bone was varied between 0.0
and 0.3.
3.4 Solution and post-processing
FEA was performed using ABAQUS/Standard software, version 6.9-1 (Dassault Simulia
Inc., RI, USA). Load-displacement data was quantified at the tip. Pile-up was defined in
terms of height above the initial upper bone surface. In the case of an indenter that does
not exhibit axial symmetry, such as the Berkovich indenter modelled in this study, the
pile-up varies circumferentially. Therefore, for the 3D models, vertical displacement of
the upper bone surface was viewed from above (X-Z plane, see Figure 1) as well as
from different cross-sections rotating about the centre axis of the one sixth model.