Biomedical Engineering Reference
In-Depth Information
Fig. 23.6
Left
: schematic
representation of the
compression test.
Right
:
representation of the mesh for
the compression test
23.4 Results
23.4.1 Shear Test Using Discontinuous Chemical Potential
(Case 1)
For the shear test the sample is boxed except for the contact area with the piston.
On the right the sample is in contact with a filter, which causes an equilibrium with
an external salt solution (
μ
in
=
μ
ex
) and concomitant prestress is all directions. An
initial crack is imposed away from element interfaces (Fig.
23.6
).
The material properties are given in Table
23.1
. External load is applied through
the piston. The piston is moved with constant speed
v
10
−
3
mm
/
s. Crack
growth is investigated in a free swollen sample. The initial size of the sample is the
result of free swelling in both directions. The resulting pre-strain is
ε
ix
=
=
0
.
15
·
·
10
−
3
.InFig.
23.7
the distribution of the chemical potential is given. The movement
of the piston results in initially straight crack growth which after a while deflects.
At the crack tip a pressure gradient over the crack exists.
The fluid flow evolution in case of free swelling is considered across the crack
ε
ix
=
1
.
2
n
+
=
0
.
48 mm), see Fig.
23.8
. The flow in the initial crack is nonzero. Every time the
crack propagates a peak in flow takes place which is also felt in the already existing
crack. The crack grows for several elements after which stress is built up again and
in which the flow relaxes. The fluid flow is nonzero from start. When the local per-
meability is taken constant and similar to bulk permeability (
k
d
=
K
d
), the overall
crack propagation is not changed much, but fluid exchange is lower and more slowly
initiated. When the permeability is taken much lower, there is hardly any fluid flow.
There are two types of discretization sensitivity: in time and in space. Decreas-
ing the time discretization by a factor 4 does not have any influence on bulk and
crack behavior. Therefore, the time step is sufficiently small. Decreasing the mesh
discretization size by a factor two, does not have a negligible effect. Decreasing
the mesh size, but keeping the nonlocal length
l
a
(Eq. (
23.37
)) constant, increases
the amount of integration points over which the stress at the crack tip is averaged.
·
=
q
for two points, in the initial crack (d
x
0
.
28 mm) and in the crack (d
x
