Nonlinear Finite Element Analysis of Concrete Structures

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with in a correct way. Eventually, and as a very important feature,
the model should be easy to calibrate to a particular type
of concrete. For instance it is very advantageous if all parameters
are calibrated by means of uniaxial data alone.
A model reflecting most of the above-mentioned features will be
described in the following, but prior to this attention will be
turned towards the large number of proposals for predicting the
nonlinear behaviour of concrete that have appeared in the past.
Plasticity models have been proposed; however because of their
simplicity the bulk of the models are nonlinear elastic ones. A
review of some models is given as follows:
Plasticity models based on linear elastic-ideal plastic behaviour
using the failure surface as yield surface have been proposed
by e.g. Zienkiewicz et al. (1969), Mroz (1972), Argyris
et al. (1974) and Willam and Warnke (1974). A somewhat different
approach still accepting linear elastic behaviour up to failure
was put forward by Argyris et al. (1976) using the modified Coulomb
criterion as failure criterion. Instead of a flow rule this
model uses different stress transfer strategies when stresses
exceed the failure state. A very essential feature is that different
post-failure behaviours can be reflected in the model. To
consider the important nonlinearities before failure, models
using the theory of hardening plasticity have been proposed by
e.g. Green and Swanson (1973), Ueda et al. (1974) and Chen and
Chen (1975), all of whom neglect the important effect of the
third stress invariant, while Hermann (1978) includes the effect.
However, as these plasticity models all make use of Drucker's
stability criterion (1951) they are not able to consider the
strain softening effects occurring after failure. Coon and Evans
(1972) applied a hypoelastic model of grade one, but this model
also operates with two stress invariants only, and strains are
inferred as infinite at maximum stress.
Incremental nonlinear elastic models based on the Hookean anisotropic
formulation have been proposed for plane stress by Liu
et al. (1972) and Link et al. (1974, 1975). The model of Darwin
and Pecknold (1977) applicable for plane stresses can even be