Biomedical Engineering Reference
In-Depth Information
And again for a uniaxially loaded bar
σ
R
=
σ
ax
. For an arbitrary stress state
the equivalent stress according to Rankine can be completely different from the
equivalent stress according to Tresca or von Mises.
A few remarks on this subject are opportune at this point. The understanding of
failure thresholds and mechanisms for biological materials involves much more
than identifying a suitable equivalent stress expression. Biological materials can
also fail because of a disturbance of the metabolic processes in the cells. The
mechanical state in biological materials is not only determined by stresses and
strains, but also by rather complicated transport processes of nutrients, oxygen and
waste products and very complex biochemistry. These processes can be disturbed
by mechanical deformation (for example occlusion of blood vessels, causing an
ischemic state of the tissue, resulting in lack of oxygen and nutrients and accu-
mulation of waste products). After some time this may result in cell death and
thus damaged tissues. How these processes evolve and lead to tissue remodelling
and/or damage is still the subject of research.
Exercises
8.1
Consider a two-dimensional plane stress state, with stress components:
σ
xx
=
ax
2
+
by
σ
yy
=
bx
2
+
ay
2
−
cx
.
Use the equilibrium equations to determine the shear stress component
σ
xy
(
x
,
y
), satisfying
σ
xy
(0,0)
=
2
a
.
8.2
On an infinitesimal area segment, stress components are working as given
in the figure.
20
5
5
10
10
5
y
5
x
20
