Biomedical Engineering Reference
In-Depth Information
Ta b l e 2
Set of parameters as used in the numerical examples (n
=
M for the media and n
=
Afor
the adventitia)
Type
Symbol
Va l u e
Unit
Media
Adventitia
R
i
,
1
Geometrical
1.35
1.89
mm
H
1
0.54
0.36
mm
R
i
,
2
1.55
1.97
mm
H
2
0.42
0.28
mm
L
1
2.0
mm
L
2
3.0
mm
n
Structural
ʲ
21.700
62.260
deg
n
κ
0.19
0.036
-
n
ʱ
{
0
.
0
,
45
.
0
,
{
0
.
0
,
90
.
0
,
deg
60
.
0
,
120
.
0
}
120
.
0
,
160
.
0
}
e
Elastic
μ
27.0
2.7
kPa
e
ʺ
2700.0
270.0
kPa
k
1
0.64
5.1
kPa
k
2
7.08
30.8
-
kPa
−
1
mm
2
Regularisation
c
d
{
0
.
08
,
0
.
5
,
3
.
0
}
kPa
−
1
ʲ
1000
.
0
d
kPa
−
1
Damage
ʷ
0
.
25
d
ʺ
5
.
0
kPa
d
cos
ʲ
n
e
ʘ
with n
A for the adventitia. The perfect
tube is discretised by 800, the perturbed tube by 12,000 finite elements. Since we
prescribe the radii
R
i
of the opened configuration and the opening angles
=
M for the media and n
=
n
as input
parameters to create the residual strain field, we expect to reproduce these values at
least approximately as well as a complete stress release at the end of the simulation.
Basically the FE-simulation of the opening angle experiment is subdivided into a
sequence of two calculation steps:
ʱ
1.
Application of the residual strain field
at Gauss-point-level: apply homogeneous
Dirichlet boundary conditions at all nodes in circumferential and axial direction.
2.
Radial cut
: apply homogeneous Dirichlet boundary conditions at two nodes in
radial direction, at all nodes located at the cut in circumferential direction and at
all nodes at back face in axial direction.
In this regard, all boundary conditions are removed from one step to another and re-
specified for those boundary conditions that are to be retained. If a boundary condition
is removed, it will be replaced by a concentrated force equal to the reaction force
calculated at the restrained degree of freedom at the end of the previous step. This
concentrated force will then be linearly reduced to zero over the period of the step. In
this case, both layers are separated fromeach other in order to give an illustrative view
