Biomedical Engineering Reference
In-Depth Information
Fig. 11 Mechanics of uni-directional tissues: experimental along-t constitutive response of rat
tail tendons [
27
,
61
] compared with the numerical results obtained via present model by using two
consistent sets of micro/macro model parameters (Table
1
). r
t
;
t
and e
t
;
t
denote direct stress and
strain components, respectively, along the fiber-chord direction t. The shape of the collagen fiber
centerline in the reference configuration is defined as in Eq. (
20
) with v
¼
0. Values of nanoscale
model parameters are set equal to:
'
p
¼
14
:
5 nm,
'
c
¼
287 nm, E
o
¼
1 GPa, E
¼
80 GPa,
g
¼
22
:
5, e
o
¼
0
:
1
;'
kinks
¼
14 nm, A
m
¼
1
:
41 nm
2
, T
¼
310
:
15 K, l
¼
1
;
kk
cl
¼
10 pN/nm
Table 1 Values of micro- and macroscale parameters for tendons employed in numerical
applications with relevant references
H
o
=
L
o
r
F
=
L
o
L
o
(lm)
V
f
E
M
(MPa)
m
M
Set 1
0.05
0.02
200
50 %
1
0.49
Set 2
0.0635
0.0325
Ref.
[
28
]
[
29
]
[
27
,
28
]
[
30
]
[
62
]
[
62
]
ð
e
F
Þ
e
t
¼
^
T
r
ð
t
Þ
~
ð
e
F
Þ½
^
T
e
ð
t
Þ
1
e
t
;
r
t
¼
C
C
ð
29
Þ
^
^
where
T
e
ð
t
Þ
are the stress and strain transformation matrix from the
local to the global coordinate system, and e
t
, r
t
are the increments of macro strain
and stress vectors (in Voigt notation) for the equivalent homogeneous tissue,
respectively.
In order to validate the present approach, uni-axial traction along the fiber-
chord direction of tendinous tissues is addressed, comparing available experi-
mental data for rat tail tendons with numerical results obtained via the proposed
model. Figure
11
shows the excellent agreement between experimental results
measured from two different tendinous specimens [
27
,
61
] and the model's out-
comes. These are obtained by using an incremental approach and considering two
different sets of parameters (Table
1
). The major issue is that, setting the same
values for nanoscale parameters (since the collagen-related nanoscale features are
similar among different healthy tissues), different tissue mechanical responses are
clearly reproduced by considering differences in microscale fiber geometry.
T
r
ð
t
Þ
and
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