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

IS 3D FINITE ELEMENT ANALYSIS OF NANOINDENTATION
NECESSARY TO INVESTIGATE POST-YIELD MECHANICS OF
BONE?
1. ABSTRACT
V. R. Toal 1 and C. J. Adam 2
Nanoindentation is used to probe the micromechanical properties of bone. Finite
Element Analysis (FEA) of nanoindentation can extend the conventional mechanical
property output to develop constitutive models of bone’s post-yield behaviour. It has
been shown that load-displacement curves are almost equivalent for two-dimensional
(2D) axisymmetric and three-dimensional (3D) FEA models, but the same cannot
necessarily be said for 2D versus 3D simulations of pile-up surrounding the indent.
Furthermore, it has been suggested that friction between the indenter and bone, often
assumed negligible, may be an important consideration for nanoindentation simulations.
Accordingly, the aim of this study was to compare the pile-up predicted by 2D
axisymmetric and 3D models of bone nanoindentation using the three-sided pyramidal
Berkovich tip, including the role of friction.
Two series of FE analyses were performed using solid continuum 2D axisymmetric and
3D hexahedral elements on bone block meshes, refined at the point of indenter contact.
The equivalent conical angle of 70.3° was used for the axisymmetric model, while the
3D model consisted of one sixth of the indenter with half angle of 65.35°. Both models
included a tip radius of 150 nm and an elastic-perfectly plastic material model with von
Mises yield surface (E = 13.56 GPa, υ = 0.3, σyield = 301 MPa) to simulate a
displacement-controlled indentation to 2.55 µm. The frictional coefficient between
indenter and bone was varied between 0.0 and 0.3.
The resulting load-displacement curves varied little between the axisymmetric and 3D
models, consistent with existing literature. However, the 3D model pile-up height was
up to 40% greater than the axisymmetric model. These results suggest that
characterising bone plasticity through FE modelling of nanoindentation may require a
three-dimensional approach.
2. INTRODUCTION
Physiological and abnormal mechanical loading of the skeleton can lead to the
formation of microdamage, tiny cracks within the bone tissue [1]. This is the physical
manifestation of post-yield loading of bone tissue and has been implicated as a
contributing factor to bone fragility [2]. Nanoindentation of bone has become a popular
approach in recent years to probe the micromechanical properties of the tissue, the scale
1 PhD Candidate. 2 Associate Professor. School of Chemistry, Physics and Mechanical Engineering,
Science and Engineering Faculty, Queensland University of Technology, Gardens Point, Brisbane,
Queensland 4000, Australia