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

at which microdamage originates. For instance, it has been used to investigate the
mechanical role of components that make up bone tissue [3].
Given the technical difficulties of experimentation with miniature bone samples, as well
as ethical and safety concerns, numerical simulation of mechanical experiments can
complement the understanding of the response of healthy and diseased bone to
mechanical loading. Finite Element Analysis (FEA) can be used to further understand
how microdamage occurs and the material properties of natural bone, which in turn may
improve the design of implants and artificial bone material substitutes.
FEA of bone nanoindentation is used to explore the post-yield properties of bone tissue,
providing an extension to the indentation modulus and hardness values that are typically
reported from nanoindentation, such as constitutive modelling approaches [3-6].
Recently the role of friction in such simulations has been highlighted as important in
determining the post-yield response of bone tissue to indentation loading [6].
Due to the high computational cost associated with three-dimensional (3D) models of
nanoindentation, idealised two-dimensional (2D) axisymmetric models are often used
[4, 6]. Especially as material models required to fully describe the post-yield nature of
bone tissue become more complex with increased computational time to solution, an
axisymmetric simplification may be desirable. However, such a 2D idealisation may not
adequately capture the deformation (in particular the pile-up characteristics) of the bone
tissue with an indenter that does not exhibit axial symmetry. Accordingly, the aim of
this study was to compare the pile-up predicted by both axisymmetric (2D) and threedimensional
(3D) models of bone nanoindentation using the three-sided pyramidal
Berkovich tip, including the role of friction.
3. METHODS
3.1 Geometry and FE mesh
Two meshes were generated to compare the prediction by 2D axisymmetric and 3D FE
models of pile-up of bone undergoing nanoindentation with a Berkovich indenter.
Cylindrical bone blocks of equal height and radius, 150 µm and 200 µm for the 2D and
3D models respectively, were meshed with solid continuum elements. The 2D
simplification employed linear 4-node reduced integration axisymmetric elements
(ABAQUS CAX4R), while the 3D model contained linear 8-node reduced integration
hexahedral elements (ABAQUS C3D8R). The mesh was refined at the indenter tip
contact and pile-up regions, as shown in Figure 1. Due to six-fold symmetry of the
Berkovich indenter, one sixth of the bone block was sufficient for the 3D model.
Aiming for similar meshing characteristics, the vertical face of the 3D model was
meshed corresponding to the 2D model and revolved through the bone block.
Preliminary mesh sensitivity analysis showed the tip reaction force and pile-up
measurements were not influenced by domain size. In each simulation, the indenter was
modelled as a rigid body analytical surface. Based on Lichinchi et al. [7] an equivalent
conical angle of 70.3° was used for the 2D model, while the 3D model consisted of the
true Berkovich indenter half angle 65.35° (Hysitron Inc., MN, USA). Both models had a
tip radius of 150 nm.