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

cortical thickness only). The values used are shown in Table 1 [6].
Table 1 – Material properties of the bone
Young / Healthy Old / Osteoporotic
periosteum endosteum periosteum endosteum
E11 18.6 16.6 12.9 3.2
E22 18.8 17.1 14.6 6.0
E33 22.4 21.4 19.3 11.2
G12 7.2 6.6 5.4 1.8
G13 6.9 6.4 5.4 2.2
G23 7.0 6.5 5.7 3.0
v12 0.29 0.27 0.24 0.16
v13 0.26 0.24 0.20 0.07
v23 0.26 0.24 0.22 0.14
The heterogeneity was modelled using a temperature gradient from the periosteum to
the endosteum and applying tensorally interpolated material properties accordingly. The
anisotropy was incorporated using cylindrical axes for each segment of the crosssection.
The plate and screws were assumed to be homogeneous, isotropic and linear elastic
steel. The Young’s moduli for both were 1.80x10 11 N/m 2 [7-10]. Poisson’s ratio for
steel was taken as 0.3 [9-11].
Both linear and nonlinear models have been considered for friction between the bone
and the implant [5, 7, 12-15]. The screw-bone interaction at the entrant cortex was
modelled as frictional using a standard Coulomb friction coefficient of 0.3 based on
some of the recent studies [13, 14]. As the majority of load is transferred at the screw
holes on the entrant cortex the screw-bone interaction at the exit cortex was modelled as
tied for analysis simplification. The plate-bone interaction used a frictional coefficient
of 0.4 [2].
The load was applied as prescribed axial displacement at the free end. The analysis was
conducted up to a load of 1891N which is approximately 2.6 times bodyweight for a
75kg person. Patient weight bearing force in the tibial mid shaft has been shown to be
up to 2000N at 10 weeks and 2500N at 16 weeks after surgery [16].
The screw fastening preload was represented using thermal contraction. A thin slice of
the screw shaft, below the head and above the first thread, was shrunk and contraction
was only permitted in the desired direction (axially); transverse and shear expansions
were set to zero. The coefficient of expansion was calculated using trial and error until
the net tensile force generated in the screw was 500N. Similarly, the plate was shrunk to
induce compression at the fracture gap to a value of 500N. Values of screw axial force
and plate tension generated during screw fastening vary widely in the literature. The
values chosen was based on an average of some previous studies [2, 3, 17, 18].
The fastening preload induced by the thermal contraction was compared with other
studies. The load sharing of the threads was found to be similar to an FE screw pullout
study by Gefen et al. [8] and to analytical models by Grewal et al. [19], with the
proportion of load taken by threads decreasing down the shaft.