Biomedical Engineering Reference
In-Depth Information
Fig. 8 Actual fiber configuration at e
F
¼
0
:
1(continuous lines) for different reference centerline
shapes (dotted lines) corresponding to x
¼
0(top left), x
¼
2(top right), x
¼
4(bottom left),
and x
¼
8(bottom right). Parameters: H
o
=
L
o
¼
0
:
1
;
r
F
=
L
o
¼
0
:
025
;
L
o
¼
100 lm, v
¼
0
:
1
response related to the decrease of the fiber crimp is highlighted in Fig.
9
, wherein
the centerline shape is proved to affect the fiber mechanical response mostly for
high values of the aspect ratio H
o
=
L
o
, resulting in a significant dependence on the
parameters v and x.
The fiber behavior is highly non-linear because of both material (at nanoscale
and mesoscale) and geometric effects. Nevertheless, if the equivalent modulus E
eq
is normalized with respect to the fibril's one E
f
, the effects related only to geo-
metric non-linearities can be highlighted. Accordingly, Fig.
10
shows the influence
of the shape parameters (H
o
=
L
o
;
x, and r
F
=
L
o
) on the fiber mechanical response
related to geometric non-linearities, in terms of the tangent modulus in the
reference configuration (i.e., at e
F
¼
0) as well as in terms of modulus variation
versus the fiber strain level e
F
.
7 Macroscale Mechanics
Previous microscale approach is employed to describe the mechanical behavior of
collagenous fibers within regular soft tissues. Fibers are assumed to be embedded
into a linearly elastic isotropic matrix, whose Young modulus and Poisson ratio are
E
M
and m
M
, respectively. Neglecting any fiber-matrix interaction effect, crimped
fibers are reduced to equivalent reinforcing straight fibers, exhibiting an elastic
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