Civil Engineering Reference
In-Depth Information
- the second invariant, the von Mises equivalent stress;
3
V
J
V
ss
:
[2.25]
eq
2
2
- the third invariant, i.e. Lode's angle;
1
33
J
1
1
1
3
3
3
3
[2.26]
J
trace
V
VV V
cos 3
T
3
ij
jk
ki
3
3
3
2
2
J
2
The criteria are generally isotropic, but they express asymmetry between traction
and compression. Among the criteria used for concrete are Coulomb's and Drucker
Prager's criteria [DRU 52].
§
·
1
3
[2.27]
f
V
s
:
s
D
trace
V
Y
0
D
¨
¸
h
¨
¸
2
2
©
¹
This criterion is now used as a reference for the shear failure of geomaterials.
More elaborate criteria, taking the third invariant into account, for example, are used
for other models. We cite those defined by Ottosen, Argyris, and Willam Warnke as
examples.
Figure 2.16.
Representation of a “cap” surface
The criteria linked to shear failure such as those below, do not express high-
pressure irreversible phenomena. In the plane of the first two invariants, the
representation of the criterion gives an “open” curve on the pressure axis. The
eponymous “cap” surface closes the elastic domain (Figure 2.16); it is associated
with compaction.
Search WWH ::
Custom Search