Biomedical Engineering Reference
In-Depth Information
s
t
y
0
+
Δ
y
s
l
s
r
y
0
s
b
e
y
e
x
x
0
x
0
+
Δ
x
Figure 8.5
Free body diagram of the infinitesimal volume element.
σ
yy
(
x
,
y
0
+
Δ
y
)
σ
xy
(
x
,
y
0
+
Δ
y
)
σ
yx
(
x
0
+
Δ
x
,
y
)
σ
xx
(
x
0
+
Δ
x
,
y
)
y
0
+
Δ
y
σ
xx
(
x
0
,
y
)
y
0
σ
yx
(
x
0
,
y
)
σ
xy
(
x
,
y
0
)
e
y
σ
yy
(
x
,
y
0
)
e
x
x
0
x
0
+
Δ
x
Figure 8.6
Stresses acting on the surfaces of an infinitesimal volume element.
action and reaction. When both the outer normal and the stress component are ori-
ented in a negative direction relative to the coordinate axes, the stress is positive.
When the normal points in a positive direction while the stress points in a negative
direction (or vice versa), the stress is negative.
Clearly, all stress components are a function of the position in space, hence
of the
x
- and
y
-coordinate (but not of the
z
-coordinate because all quantities are
assumed constant in the
z
-direction):
σ
xx
=
σ
xx
(
x
,
y
)
σ
yy
=
σ
yy
(
x
,
y
)
σ
xy
=
σ
xy
(
x
,
y
)
σ
yx
=
σ
yx
(
x
,
y
) .
(8.10)
