Biomedical Engineering Reference
In-Depth Information
(a) Calculate the strain in circumferential direction at the inner side of
the wall.
(b) Calculate the strain in the
e
x
-direction at point A at the inner side of
the vessel wall.
(c) Calculate the stress in circumferential direction at point A.
12.6 Consider a bar (length 2
L
) with a circular cross section (radius
R
). The
axis of the bar coincides with the
z
-axis of a
xyz
-coordinate system. With
respect to the mid plane (
z
0) the top and bottom plane of the bar are
rotated around the
z
-axis with an angle
=
α
(with
α
1), thus loading the
bar with torsion. See the figure.
z
L
y
x
L
The position vector
x
of a material point in the deformed configuration is
x
=
x
0
−
α
(
x
0
·
e
y
)(
x
0
·
e
z
)
e
x
+
α
(
x
0
·
e
x
)(
x
0
·
e
z
)
L
e
y
,
L
with
x
0
the position vector of that point in the undeformed state. The mate-
rial behaviour is linearly elastic according to Hooke's law, with Young's
modulus
E
and Poisson's ratio
.
Determine, for the material point defined with
ν
x
0
=
R
e
y
, the linear strain
tensor
ε
, the stress tensor
σ
and the equivalent stress, according to von
Mises
σ
M
.
