Biomedical Engineering Reference
In-Depth Information
on the spatial domain
=
[ 0 1] and a temporal domain that spans
t
=
[ 0 0.5]. At
x
=
0 the boundary condition
u
=
0 is prescribed, while at
x
=
1,
cdu
/
dx
=
0 is selected. The convection dominated case is investigated,
with
v
=
1 and
c
=
0.01. The problem is solved using the
θ
-scheme with
θ
=
0.5, a time step
t
=
0.05 and 40 linear elements.
(a)
First, the initial condition:
u
(
x
,
t
=
0)
=
sin(2
π
x
)
is considered. Adapt the
demo_fem1dcd
and the FEM program
accordingly. In particular, make sure that the initial condition is han-
dled properly in
fem1dcd
. (Hint: the initial condition is specified in
sol(:,1)
.) Solve this problem. Plot the solution for all time steps.
(b)
Second, let the initial condition be given by
u
(
x
,
t
=
0)
=
0for
x
<
0.25 and
x
>
0.5,
while
u
(
x
,
t
=
0)
=
1 for 0.25
≤
x
≤
0.5.
Solve this problem in the same way.
15.4 Many biological materials can be described as a mixture of a porous solid
and a fluid, like articular cartilage [
13
], skin [
14
], intervertebral disk [
6
],
heart tissue [
11
], etc. A confined compression test can be used to determine
the material parameters. A circular specimen is placed in a confining ring.
A porous filter supports the solid phase, while fluid from the specimen can
be expelled. On top a tight-fitting indenter is placed to mechanically load
the specimen with a constant force. Because of the confining ring the speci-
men can only deform in one direction. When a step load is applied to the
loading shaft
saline solution
tissue sample
confining ring
filter
supporting
ring
tissue, at first a pressure will be built up in the fluid. Immediately after load-
ing the fluid will start moving through the filter and the solid will gradually
take over the load. After some time the pressure in the fluid is zero and all
load is taken by the solid. It can be derived from the theory of mixtures
