Civil Engineering Reference
In-Depth Information
s
t
ck
t
u
Figure 5.26 Postfailure stress-displacement curve as given in ABAQUS [1.29].
depend on the specimen's length. This fracture energy cracking model can
be invoked by specifying the postfailure stress as a tabular function of crack-
ing displacement, as shown in
Figure 5.26
.
Alternatively, the fracture
energy,
G
f
, can be specified directly as a material property and, in this case,
define the failure stress,
s
to
, as a tabular function of the associated fracture
energy. This model assumes a linear loss of strength after cracking, as shown
in
Figure 5.27
.
The cracking displacement at which complete loss of
strength takes place is, therefore, (
u
to
¼
2
G
f
/
s
to
). Typical values of
G
f
range
from 40 (0.22 lb/in) for a typical construction concrete (with a compressive
strength of approximately 20 MPa, 2850 lb/in.
2
) to 120 N/m (0.67 lb/in)
for a high-strength concrete (with a compressive strength of approximately
40 MPa, 5700 lb/in.
2
). If tensile damage,
d
t
, is specified, ABAQUS auto-
matically converts the cracking displacement values to “plastic” displace-
ment values. The implementation of this stress-displacement concept in a
finite element model requires the definition of a characteristic length asso-
ciated with an integration point. The characteristic crack length is based on
the element geometry and formulation. This definition of the characteristic
crack length is used because the direction in which cracking occurs is
not known in advance. Therefore, elements with large aspect ratios will
have rather different behaviors depending on the direction in which they
s
t
s
to
u
to
= 2
G
f
/
s
to
G
f
u
to
Figure 5.27 Postfailure stress-fracture energy curve as given in ABAQUS [1.29].
u
t
Search WWH ::
Custom Search