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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
L. A. F. de Souza | R. D. Machado
In relation to the first simulation, the computational numerical mod-
el implemented in this work, even it being one-dimensional, was
able to reasonably reproduce the results with regards to the other
answers obtained in Jarek
et al
. [7]. The rupture load predicted
by the criterion of Tsai and Wu [18] was close to the experimental
collapse load. However, depending on the adopted value for the
reference strain
ε
d0
, the numerical answer may differ and lead to
non-satisfactory results.
Tsai and Wu’s [18] theory was chosen for presenting many advan-
tages in relation to the several other existing theories, such as: it is
a scalar and invariant equation in which the strength components
are expressed in a tensor; and the symmetry properties of the ten-
sor may be strictly determined.
The second problem is a study of the coupling of theories - Dam-
age Mechanics and Fracture Mechanics - for simulating the phe-
nomena related to the concrete behavior.
The structural analysis of reinforced concrete parts with a previous
crack (discontinuity) carried out through the line interface element, –
for simulating the crack - together with a model of damage, has proved
to be satisfactory from the qualitative point of view, for the maps of the
damage distribution once all the simulations presented perpendicular
cracks to the pull rod axis and parallel among themselves.
This methodology has the advantage of not requiring the use of
finite element mesh reconstruction techniques. In general, discreet
models require sophisticated and expensive mesh reconstruction
techniques, from the computational point of view, for capturing the
propagation of cracks along the loading process.
It is believed that the adoption of constitutive models that consider
the coupling of theories present a great potential for projects used
for calculating the collapse load and identifying all the mechanism,
for verifying the behavior of finite elements under stress and in the
analysis of reinforced concrete structures subject to random loads,
for instance, the ones from the shocks, and also for verifying the
deformability of the structures in use.
The joint application of such models in practical situations is
harmed due to the experimental identification of the parameters
contained in the evolution laws of the damage and fracture vari-
ables. According to Pituba and Proença [13], the Mazars’ [10]
model can be expanded for use in situations that are more close
to reality, provided that resources such as the armatures plastifica-
tion, location of permanent strains and the consideration of the in-
teraction between the concrete and the armature are incorporated.
In future works, besides the suggestions from these authors, we
intend to implement new constitutive models based on the Con-
tinuous Damage Mechanics for simulating the concrete and other
failure criteria, such as the Willian-Warnke, in two-dimensional and
three-dimensional reinforced concrete structures, which will allow
more realistic analyses.
9. Bibliography
[01] ÁLVARES, M. S.; PROENÇA, S. P. B.; BILLARDON,
R. Estudo e emprego de um modelo de dano localizado:
aplicação a vigas em concreto armado. In: XX
CILAMCE - Congresso Ibero-Latino Americano
Sobre Métodos Computacionais para Engenharia,
São Paulo, 1999.
[02] BESSA, V. M. R. d’A.; QUININO, U. C. M.;
BITTENCOURT, E.; ITURRIOZ, I. Análise da
fissuração de um tirante de concreto simples -
comparação de diferentes metodologias. In: V
Simpósio EPUSP sobre Estruturas de Concreto,
São Paulo, 2003.
[03] GAGLIARDO, D. P.; GAGLIARDO, J. C.; MASCIA,
N. T. Comparação entre os critérios de Rankine e de
Tsai Wu para uma viga de concreto reforçado com
fibras. In: Anais do 53º Congresso Brasileiro do
Concreto - CBC 2011, Florianópolis, SC, 2011.
[04] GUELLO, G. A. Simulação computacional de estruturas
de concreto por meio da mecânica do dano. Dissertação
(Mestrado), Escola Politécnica da Universidade de
São Paulo, São Paulo, 2002.
[05] GUELLO, G. A.; BITTENCOURT, T. N. Simulação
Computacional de Estruturas de Concreto por meio da
Mecânica do Dano. Boletim Técnico da Escola
Politécnica da USP, São Paulo, v. 202, n. 1, p. 1-12, 2002.
[06] HILL, R. A Theory of the Yielding and Plastic Flow of
Anisotropic Metals. In: Proceedings of the Royal
Society of London, Series A, London, v. 193,
p. 281-297, 1948.
Figure 5 – Damage distribution in the
concrete in the half part of the pull
rod with discontinuity for: a)
= 0.00005;
d0
b)
= 0.00003; e
= 0.00001
d0
d0