Nonlinear Finite Element Analysis of Concrete Structures

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Figure 9 contains the experimental results of Kupfer et al. (1969,
1973) for biaxial tensile-compressive loading of three different
types of concrete. Both failure stresses and failure modes are
indicated In addition, the figure shows the corresponding failure
curves together with their failure mode criteria using the
two failure criteria implemented in the finite element program.
It appears that the two failure mode criteria and the two failure
criteria are in close agreement with the experimental evidence.
In accordance with earlier conclusions the proposals of
the writer are favourable when considering accuracy. The modified
Coulomb criterion , on the other hand, possesses an attractive
simplicity.
For both failure mode criteria it is assumed that the orientation
of the crack plane is normal to the principal direction
of o.. This assumption is also in good agreement with the aforementioned
tests.
2.2. Stress-strain relations
Having discussed the strength of concrete in some detail, the
stress-strain behaviour will now be dealt with. Ideally, a constitutive
model for concrete should reflect the strain hardening
before failure, the failure itself as well as the strain softening
in the post-failure region. The post-failure behaviour has
received considerable attention in the last years especially,
where it has become evident that the calculated load capacity of
a structure may be strongly influenced by the particular postfailure
behaviour employed for the concrete; for example ideal
plasticity with its infinite ductility might be an over-simplified
model. This is just to say that redistribution o i stresses
in a structure must be dealt with in a proper way. These aspects
will be considered in some detail in section 5. Moreover, the
constitutive model should ideally be simple and flexible, i.e.
different assumptions can easily be incorporated. The numerical
performance of the model in a computer program should also be
considered. Moreover, it should be applicable to all stress
states and both loading and unloading should ideally be dealt