Biomedical Engineering Reference
In-Depth Information
on the (visible) faces of the element. The mechanical behaviour of the ele-
ment is described by the linear Hooke's law, with Young's modulus
E
=
8
3.
Determine the volume change
V
/
V
0
, with
V
0
the volume of the element
in the unloaded reference configuration and
V
the volume in the current
loaded configuration, assuming small deformations.
12.2 An element of an incompressible material (in the reference state a cube:
×
×
[MPa] and Poisson's ratio
ν
=
1
/
), is placed in a Cartesian
xyz
-coordinate system as given in the
figure below. Because of a load in the
z
-direction the height of the element
is reduced to 2
3. In the
x
-direction the displacement is suppressed. The
element can expand freely in the
y
-direction. The deformation is assumed
to be homogeneous.
The material behaviour is described by a Neo-Hookean relation, according
to:
/
G
B
d
,
σ
=−
p
I
+
σ
with
the stress matrix,
p
the hydrostatic pressure (to be determined),
I
the
unit matrix,
G
the shear modulus and
B
the left Cauchy Green deformation
matrix.
z
z
y
y
2 /3
3 /2
x
x
Determine the compressive force
F
v
in
z
-direction that is necessary to
realize this deformation.
12.3 A frequently applied test to determine the stiffness properties of biolog-
ical materials is the 'confined compression test'. A schematic of such a
test is given in the figure. A cylindrical specimen, Young's modulus
E
,
K
ν
h
R
