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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
J. J. C. PITUBA | M. M. S. LACERDA
Figure [12]. The parameters values as described in the Table [3].
Initially, the longitudinal discretization has been composed by 16
finite elements and cross section was divided into 15 layers, where
there are layers that represent the reinforcement areas located in
their barycenters, see Figure [3].
The numerical responses obtained with isotropic and anisotropic
damage models are able to simulate the experimental behavior of
the beam, see Figure [13]. Both damage models present a strong
loss of stiffness about 18 kN trying to evidence a possible damage
localization process. In this context, in Delalibera [17] is reported
that the first crack occurs about 25 kN. As it can be seen, the
numerical responses are quite satisfactory when compared to the
experimental results since the beginning of the damage process
up to the complete rupture of the beam.
On the other hand, it is noted that the numerical responses pres-
ent a difficulty of convergence evidenced by the increase of the
iterations about 115 kN. In this stage, the concrete presents high
values for the damage variables in many layers of finite elements
located in the medium zone of the beam, therefore the beam stiff-
ness is mainly due to the reinforcement bars.
5. Conclusions
The study concerns to the employment of anisotropic and isotropic
damage models to one and two-dimensional concrete structure
analyses. In a general way, the numerical results obtained from
the damage models presented in this work have been quite satis-
factory. The potentialities of the Damage Mechanics when deals
with numerical simulation of the non-linear behavior of concrete
structures are shown. In particular, the employment of anisotro-
pic models has shown some advantages in 2D analysis when
Figure 12 – Parametric identification in uniaxial compression and tension tests
for reinforced concrete beam
Uniaxial Tension Test
Table 3 – Parameter values – reinforced concrete beam
Mazars’ model
Pituba’s model
Tension
Compression
Tension
Compression
A = 1,71
T
A = 2280
C
Y = 1,137x10 MPa
01
-4
-5
Y =5,0x10 MPa
02
B = 11300
T
B = 12800
C
A = 5,33
1
A = 0,0086
2
e = 0,0000675
d0
-1
B = 5660 MPa
1
-1
B = 5,71 MPa
2
Figure 13 – Experimental and 1D numerical
responses of the reinforced concrete beam