Biomedical Engineering Reference
In-Depth Information
table 9.1
relationships between ash density and elastic modulus
ash density (g/cm
3
)
young's modulus (mPa)
ρ = 0
0.001
0 < ρ ≤ 0.27
33,900 ρ
2.20
0.27 < ρ ≤ 0.6
5307 ρ + 469
0.6 < ρ
10 200 ρ
2.01
Source:
J. H. Keyak, S. A. Rossi, K. A. Jones, and H. B. Skinner,
J Biomech,
31, 125-33, 1998. With permission.
Stress
E
u
Compression
Tension
Strain
ε
T
ε
t
T
E
FIgure 9.1
Schematic of the bilinear constitutive model of one bone material (not to scale).
9.2.4 n
onlinear
f
inite
e
lement
a
nalySiS
for
tHe
e
Stimation
of
f
femoral
S
trenGtH
In this chapter, two typical proximal femur models (model A and model B) were built to esti-
mate their strengths and failure locations and types. Nonlinear FE analyses were performed using
ABAQUS finite element software. The models were meshed with 261,784 and 289,362 four-node
tetrahedral elements, respectively (Figure 9.2). A distributive pressure load with a maximum mag-
nitude of 6.5 N/mm
2
was applied on the femoral head, tilting the specimen 8
o
in the frontal plane
(Gong et al., 2012). The distal end of the model was constrained. Figure 9.2 shows the FE models
with boundary and loading conditions.
The load when at least one element in the outer cortical surface yielded was used to describe
femoral strength (Bessho et al., 2007). The maximum principal strain criterion was used to judge
bone failure (Schileo et al., 2008), that is, failure of a surface element would occur in tension when
the maximum principal strain exceeded 1.174%, or in compression when the minimum principal
strain was less than -0.73% (Gong et al., 2012).
9.3 reSultS From the model analySIS
The femoral strengths predicted from nonlinear FE analyses for models A and B in Figure 9.2 were
3033.85 N and 2056.00 N, respectively. An initial tensile yield in the superolateral aspect of the
outer cortical surface of the femoral neck was predicted for model A. The initial plastic strain in this
model is shown in Figure 9.3a. For model B, an initial compressive yield in the femoral neck was
predicted and the initial plastic strain in this model is shown in Figure 9.3b.
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