Nonlinear Finite Element Analysis of Concrete Structures

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used for cyclic loading in the post-failure region. In contrast
to these proposals, similar models that now assume the incremental
isotropic formulation neglect the stress-induced anisotropy,
and softening and dilatation cannot be dealt with. This is because
tangential values of Young's modulus and Poisson's ratio can
never become negative or larger than 0.5, respectively. However,
a tangential formulation facilitates the numerical performance
regarding convergence in a computer cjde. A model based on this
incremental and isotropic concept and applicable for general
plane stresses was introduced by Romstad et al. (1974) using a
multilinear approach. In the models proposed by Zienkiewicz et
al. (1974) and Phillips et al. (1976) the tangential shear irodulus
variates as a function of the octahedral shear stress
alone. In principle, a similar approach applicable for compressive
stresses and valid until dilatation occurs was later applied
by Riccioni et al. (1977), but in this model the influence of
all the stress invariants on both the tangential bulk modulus
and the tangential shear modulus was considered. Recently, Bathe
and Ramaswamy (1979) proposed a model considering all stress invariants
also and applicable for general stress states while the
Poisson ratio was assumed to be constant.
Several nonlinear elastic models of the Hookean isotropic form
using the secant values of the material parameters have also
been put forward. An early proposal of Saugy (1969) considered
the bulk modulus as a constant and the shear modulus as a function
of the octahedral shear stress alone. For plane compressive
stresses Kupfer (1973) and Kupfer and Gerstle (1973) assumed both
these moduli to be functions of the octahedral shear stress. PTlamiswamy
and Shah (1974) and Cedolin et al. (1977) proposed nudels
applicable to triaxial compressive stress states also. Hovever
only the influence of the first two stress invariants on
the bulk and shear moduli are considered and the validity of the
models is limited to stress states not too close to failure. Also
the recent approach by Kotsovos and Newman
(1973) neglects the
influence of the third invariant. Schimmelpfennig (1975, 1976)
made use of a model where the shear modulus changes. All stress
invariants are considered but only compressive stress states can
be dealt with, and dilatation is excluded.