Nonlinear Finite Element Analysis of Concrete Structures

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question violates the failure criterion.
As a nonlinear elastic model for concrete is employed here,
loading and unloading follow in principle identical stressstrain
curves. However, as a result of the above-mentioned numerical
procedure, unloading follows the straight line from the
stress point in question towards the origin. This is illustrated
in fig. 4 and even though this unloading behaviour is still a
Fig. 4.6-4: Loading and unloading behaviour of
concrete model (fracturing solid)
very crude approximation to reality it is certainly preferable
to the ie'eal nonlinear elastic behaviour. Indeed, the behaviour
shown in fig. *• is classified as a fracturing solid according
to Dougill (1976).
It should be noted that as the secantial values of Young's modulus
and Poisson's ratio as determined by the constitutive
equation steadily decreases and steadily increases, respectively,
as the stress state approaches failure, the procedure outlined
above is always numerically stable and convergent.
Considering embedded reinforcement the program determines the
total concrete strains which in turn determine the corresponding
initial stresses in the reinforcement as described previously.
If these initial stresses have changed more than 1% the new initial
stress values are then employed and a corresponding modification
of the force vector F is carried out.