Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
f
d
[-]
1.00
0.92
0.83
0.75
0.67
0.58
0.50
0.42
0.33
0.25
0.17
0.08
0.00
(d)
(e)
(f)
f
d
[-]
1.00
0.92
0.83
0.75
0.67
0.58
0.50
0.42
0.33
0.25
0.17
0.08
0.00
Fig. 7
Perturbed tube subjected to internal pressure and residual stresses. Contour plots of
f
d
with
ʱ
M
A
=
0
.
08
[
kPa
−
1
mm
2
=
120
.
0
[
deg
]
,
ʱ
=
160
.
0
[
deg
]
,and
c
d
]
. Successive snapshots along
the unloading path at pressure levels
p
={
.
,
.
,
.
}[
]
61
08
42
89
36
33
kPa
.(
a
-
c
) associated with 3,000
elements; (
d
-
f
) associated with 12,000 elements
path. It becomes apparent that smaller values of
c
d
cause the damage distribution to
be more localised towards the thinner portion of the tube.
Finally, Fig.
7
shows the evolution of the damage function
f
d
for the prestressed
tube for
M
A
kPa
−
1
mm
2
. Three
successive snapshots along the unloading path are shown in Fig.
7
a-d which corre-
spond to pressure levels of
p
ʱ
=
120
.
0
[
deg
]
,
ʱ
=
160
.
0
[
deg
]
and
c
d
=
0
.
08
[
]
for a discretisation of
3,000 elements. We observe that damage is first initiated at the thinnest section of
the tube and later on evolves across the structure. Figure
7
d-f show the same quanti-
ties for a finer discretisation of 12,000 elements. No substantial differences between
both discretisations can be observed. Moreover Fig.
5
d shows the load-displacement
curves for both discretisations and again both curves almost completely coincide.
This underlines the mesh-objective properties of the present gradient-enhanced dam-
age model.
={
61
.
08
,
42
.
89
,
36
.
33
}[
kPa
]
