Nonlinear Finite Element Analysis of Concrete Structures

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I
a) b)
Pig. 4.6-3: Performance of the initial stress method for
\) Slightly curved stress-strain curve
b) Stress-strain curve with an almost flat part.
modifications of the force vector F has been employed here.
Tracing the nonlinear behaviour of a structure starts with a
linear elastic solution. At the load level in question, concrete
stresses determine whether cracking occurs and they also determine
those secant values of Young's modulus, E , and Poisson's
ration, v , that are in accordance with the constitutive equations.
If the utilized value of Young's modulus E is 5% larger
than the E -value then a new Young's modulus equal to 0.95 E is
employed. Likewise, if the utilized Poisson's ratio v is 5%
smaller than the v -va A ue then a new Poisson's ratio equal to
1.05v is employed. The same alternation of the two material parameters
occurs if the stress state violates the failure criterion
provided that no cracking occurs. In the post-fåilure region
when softening occurs if the utilized Young's modulus E is
smaller than the E -value a new modulus equal to 0.95 E is utilized
and at the same time Poisson's ratio v is increased to
i.05v. However, to avoid ill-conditioning of the equation system
the maximum allowable value of Poisson's ratio is set at
0.45 in accordance with the findings of Huang (1969). For crushing
of the concrete it is also possible in the program to disregard
softening in the post-failure region. This extreme assumption
of no-softening corresponds to infinite ductility at
failure and, as above, the actual values of E and v are decreased
and increased 5%, respectively, if the stress state in