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Dynamic Properties of Cortical Bone Tissue: Impact Tests and
Numerical Study
Adel A. Abdel-Wahab
a
and Vadim V. Silberschmidt
b
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University,
Loughborough, Leicestershire, LE11 3TU, UK
a
a.a.mohamed@lboro.ac.uk,
b
V.Silberschmidt@lboro.ac.uk
Keywords: cortical bone; dynamic; impact; finite-element; Izod test.
Abstract. Bone is the principal structural component of a skeleton: it assists the load-bearing
framework of a living body. Structural integrity of this component is important; understanding of its
mechanical behaviour up to failure is necessary for prevention and diagnostic of trauma. Bone
fractures occur in both low-energy trauma, such as falls and sports injury, and high-energy trauma,
such as car crash and cycling accidents. By developing adequate numerical models to predict and
describe the deformation and fracture behaviour up to fracture of a cortical bone tissue, a detailed
study of reasons for, and ways to prevent or treatment methods of, bone fracture could be
implemented.
This study deals with both experimental analysis and numerical simulations of this tissue and its
response to impact dynamic loading. Two areas are covered: Izod tests for quantifying a bone’s
behaviour under impact loading, and a 3D finite-element model simulating these tests. In the first
part, properties of cortical bone tissue were investigated under impact loading condition. In the
second part, a 3D numerical model for the Izod test was developed using the Abaqus/Explicit finite-
element software. Bone has time-dependent properties – viscoelastic – that were assigned to the
specimen to simulate the short term event, impact. The developed numerical model was capable of
capturing the behaviour of the hammer-specimen interaction correctly. A good agreement between
the experimental and numerical data was found.
Introduction
Bone is one of the most challenging natural materials that provide a structural support of the body.
Therefore, its structural integrity is significant. Bone fractures have significant health, economic
and social consequences. Both healthy and unhealthy bones are susceptible to fracture due to low-
or high-energy trauma. High-energy trauma involves, for instance, car or cycling accidents, whereas
low-energy trauma, such as falls, contact sports. When loads are applied to whole bones they
exhibit structural behaviour. Factors such as the mass of bone, its material properties and geometry
as well as the magnitude and orientation of the applied loads affect this behaviour. Bones are
fractured when they are exposed to rigorous loads that in turn generate stresses exceed its ultimate
strength. Thus, a fracture event occurs initially at the material level that eventually affects the load
carrying capacity of the whole bone at its structural level. To investigate the fracture of bone at the
material level, a set of parameters that indicates its behaviour is required [1]. It is worth mentioning
that bone is viscoelastic material. Therefore, this variant has to be considered when dealing with
spontaneous events, such as impact.
Numerous previous studies have been devoted to analysis of quasi-static mechanical properties of a
cortical bone tissue, but less attention has been paid to its dynamic mechanical characterization. A
few papers were found in the literature dealing with dynamic properties of this tissue. For instance,
both dynamic and static material properties of a human femur were investigated using a split
Hopkinson bar technique and tests with a universal testing machine [2]. The average dynamic
Young’s modulus of 19.9 GPa was found to be 23% greater than that for static loading - 16.2 GPa.
More recently, the effect of the strain rate on the mechanical properties of human cortical bone was
investigated by Hansen et al. [3]. The results of that study showed a strong effect of the strain rate
on the post-yield deformation than on macroscopic yielding initiation. In addition, the yield and
failure stress as well as the failure strain decreased for strain rates higher than 1 s
-1
. Furthermore,
strain at yield was invariant and started to decrease after strain rate higher than 10 s
-1
. Another study
by the same research group and based on the fact that the impact energy absorption capacity of bone
declines, and its mineral content increases with age [4]. Therefore, Currey et al. [5] studied the
behaviour of human femoral bone under quasi-static and impact loading and their relations to
mineral content. Though a good correlation was found between the impact absorption energy and
the work of fracture; however the changes in mineral content alone does not explain the degradation
in toughness and probably some other features associated with age which degrade the mechanical
quality of compact bone.
In terms of bone impact characteristics, only preliminary data are available in the literature. For
instance, Panagiotopoulos et al. [6] used a Charpy impact test to measure the energy absorbed by
strips cut from proximal femur and its relation to age and gender. In a related experimental work,
studying cases of fall, in-vitro bone toughness was determined as an area under the load-
displacement curve obtained in tensile/compression tests using a very low strain rate [7]. However,
the load-displacement characteristics of bone are dependent on the rate of the load. Employing an
Izod impact tester, [8] investigated the absorbed energy and the impact strength of a mandible at
different positions. Longitudinal human cortical specimens were tested in a tensile impact tester at a
strain rate of 133 s
-1
[9]. A marked non-linearity was observed in the stress-strain behaviour
including plastic deformation and strain-hardening effects. The mean tensile impact strength and
impact energy were 126.3±33.1 MPa and 18790±7355 J/m2, respectively. In a recent study, Lee et
al. [10] tested non-mineralized and mineralized materials, such as cortical bone utilizing a drop-
weight test to investigate the impact strength along with the impact damage. In a similar study,
longitudinal human cortical specimens were tested in a tensile impact tester at a strain rate of 133 s-
1 (Saha and Hayes 1976). A marked non-linearity was observed in the stress-strain behaviour,
including plastic deformation and strain-hardening effects. The mean tensile impact strength and
impact energy were 126.3±33.1 MPa and 18790±7355 J/m2, respectively. In another study,
dynamic tensile material properties of a human pelvic cortical bone were measured at different
cortex positions using a high-rate servo-hydraulic Material Testing System [11].
With an increasing number of bone fractures due to factors related to ageing, disease or dynamic
events and taking into account the complexity of bone’s mechanical behaviour, it becomes more
and more important to understand and predict this behaviour using numerical models. Though
several finite-element models were developed in the automobile industry [12, 13]; however bone
always considered as a linear-elastic material in those models. From mechanics of materials point of
view, some previous numerical models were developed using a homogenization theory to predict
macroscopic behaviour of cortical bone tissue [14, 15]. Also, a recent study [16] demonstrated
adequacy of a Double-Cantilever Beam (DCB) test for determining fracture toughness under pure
mode I loading of cortical bone by implementing a new data reduction scheme based on specimen
compliance. Despite this body of research, experimental and numerical studies of the dynamic
behaviour of a cortical bone tissue attracted less attention. Therefore, this study comprises two parts
covering experimental and numerical aspects of such analysis.
The aim of this study is to develop a numerical model to analyse the behaviour of a cortical bone
tissue under impact loading. Such a model can be used as a basis for development of more advanced
numerical tools capable to predict the behaviour of other bone tissues under arbitrary loading
conditions as well as for diseased and osteoporotic bones. To the best of the authors knowledge,
considering the modelling of cortical bone tissue at the material level under impact loading event is
no longer exist.
Methods and Materials
Specimen Preparation. Izod test’s longitudinal specimens – along osteons – were cut from fresh
bovine femora bones, (aged 1.5-2 years), see Fig.1a. Sixteen specimens were used to ensure the
reproducibility of the experimental results. All the specimens had the same dimensions (according
to ISO 180): 50 mm
×
8 mm
×
4 mm (length
×
width
×
thickness), see Fig. 1b. A 300 µm-deep notch
was created perpendicular to the bone axis and along the Radial axis direction using a razor.
Specimens were stored at room temperature in a 0.9% saline solution until tested.
(a) (b)
Fig. 1 (a) Cortical bone axes and direction of specimen cutting; (b) Izod test specimen.
Izod Test. Dynamic impact tests were carried out using a CEAST Resil Impactor. In the tests the
bottom half of the specimen was fixed firmly in the machine’s vice and a knife-edge wedge was
used to define the notch position. The upper half of the specimen was struck by a pendulum
hammer with a controlled level of energy. The distance between the notch and the position of
hammer strike was standard - 22 mm. In this study a calibrated hammer of 0.334 kg mass and
0.3268 m long was used. The nominal hammer energy of 2 J corresponds to the striking position of
150° resulting in an impact velocity of 3.46 m/s. The level of initial energy can be varied by
changing the initial angle of the hammer. Two levels of energy were used for each specimen in this
study - 0.02 J (non-destructive) and 0.5 J (destructive); they correspond to initial angles of 10° and
58°, respectively. A piezoelectric force transducer was fixed rigidly to the hammer to capture the
impact force signal. When the pendulum is released from the pre-defined angle, an impact with the
specimen generates a change in the electrical resistance of the piezoelectric sensor that is captured
by the data acquisition system - DAS 8000 - connected to the impactor.
Numerical Model
Geometry and Meshing. The impact tests were simulated with the Abaqus/Explicit finite-element
software using a 3-D formulation. The real geometry and masses of the hammer and 300 μm
notched specimen were used in simulations (see Fig. 2). The surface of the inner cylinder of the
upper block of the hammer was coupled to a reference point at the middle of that cylinder, then the
reference point was restrained to translate into x, y, and z and to rotate around x or y axes.
In simulations the initial position of the hammer was close to the specimen, its angular velocity
corresponding to the case with an initial angle of 10° (initial energy of 0.02 J). The specimen’s
support was modelled as rigid; the degrees of freedom of the specimen’s bottom part were
constrained (see Figs. 2b). Based on a convergence study, the stable time increment was 8.362×10
-
10
s and 10 nodes modified quadratic tetrahedron (C3D10M). A total number of 8472 elements and
14203 nodes for the bone specimen and 23695 elements and 6871 nodes for the hammer were used.
The force due to contact pressure between the piezoelectric force sensor and counterpart of the
specimen was requested in the history output of the finite-element software Abaqus/Explicit.
Fig. 2 (a) Izod test setup; (b) 3-D hammer-specimen assembly; (c) Hammer-specimen interaction;
(d) Hammer-specimen interaction mesh.
Material Properties. The elastic material properties for the hammer and the cortical bone tissue
used in numerical simulations are given in Table 1. The viscous behaviour of bones was introduced
into the finite-element model in terms of the Prony series expansion based on the normalized creep
compliance. These material’s constants are shear relaxation modulus ratio, g = 0.13256(±0.01) and
relaxation time, τ = 119.57(±0.5). All material properties for cortical bone were obtained in our
experiments [17]. The values used in this model were the mean values of the anterior cortex
position. The following model assumptions were made: (1) homogeneous and isotropic material
properties for both the specimen and the hammer; (2) frictionless contact between the hammer and
the specimen.
Table 1: Material properties for finite-element model
Results and Discussion
The aim of this study was to develop and verify a 3D finite-element model of Izod test setup with a
mean material data of specimen cut from the longitudinal direction of cortical bone tissue. The
intention is to develop this framework that is a step towards a more advanced model to predict the
Part
Material
Young’s modulus (GPa)
Poisson’s Ratio
Density (kg/m
3
)
Hammer
Steel
210
0.3
7850
Anterior longitudinal
Bone
23.15(±0.72)
0.44(±0.009)
1860(±0.9)
