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

AF
4. RESULTS
Table 1 Material parameters chosen from literature for both AF and NP.
The different sets of values proposed on the literature for the parameters of anisotropy
(see Table 1) raised the question of their validity and mechanical meaning. In order to
try to understand their validity, as well the reason for such large discrepancy, we have
decided to analyze the stress-stretch curves described by each set of parameters (Fig. 4).
As can be observed, the material parameters proposed by Eberlein et al. (2001) led to a
relevant discrepancy to the experimental results, which can only be understandable if an
average mechanical behavior has been assumed for all the AF. However, such
assumption can introduce some bias on the numerical results that shall be avoided in
order to take into account, in the numerical model, the role of the real gradients of
mechanical properties of fibers, either circumferentially or radially.
In addition, we selected the uniaxial tensile experimental curves published by Holzapfel
et al. (2005) for fibers located in four different regions of the AF, namely ventral and
dorsal external and ventral and dorsal internal regions using the PlotDigitizer software
(results shown in Fig. 5a).
Stress [MPa]
2.5
2.0
1.5
1.0
0.5
Refined
Parameter fit
Ventral External
Dorsal External
Ventral Internal
Dorsal Internal
0.0
1.00 1.05 1.10
Stretch ratio
1.15 1.20
Isotropy (Schmidt et al. 2007)
C 10 [MPa] 01
C [MPa] Bulk Modulus [MPa]
NP 0.12 0.03 300
AF 0.18 0.045 450
Anisotropy (Eberlein et al. 2001)
k 1 [MPa] 2
Material parameters found for graded properties
k 1 [MPa] k 2 [-]
Ventral External 12 300
Dorsal External 3 60
Ventral Internal 1.74 43.5
Dorsal Internal 0.435 8.7
a)
b)
Figure 5 a) Experimental (points) and modeled (lines) mechanical behavior for four AF regions
(ventral and dorsal, external and internal). Experimental data from Holzapfel et al. 2005. b) values of
the material parameters identified for each region of the AF.
k [-]
Dorsal fit 5 10
Ventro-lateral fit 2 190
Figure 4 Comparison between i)
the experimental mechanical
behavior for four AF regions
(ventral and dorsal external and
ventral and dorsal internal,
Holzapfel et al. 2005) and ii) the
mechanical behavior modeled by
(eq.3) with the two sets of
parameters from Eberlein et al.
2001 (Table 1) .