## Strain softening of concrete and the initiation criterion

The stress-strain relationship for concrete becomes non-linear near the peak strength [Figure 5.10-a]. In the post-peak strain softening phase, coalescence

Figure 5.10: Constitutive modelling for smeared fracture analysis; a)softening initiation criterion; b)fracture energy conservation; e)local axis system; d)closing and re-opening of cracks of the microcracks causes a gradual reduction of the stress resistance. The area under the uniaxial stress-strain curve up to the peak is taken as the index for softening initiation:

where a^ is the apparent tensile strength, that may be approximately taken 25-30% higher than the true static strength, at. It is calibrated in such a way that a linear elastic uniaxial stress-strain relationship up to aj will preserve the value U0[Figure 5.10-a].

In finite element analyses, a linear elastic relationship is assumed until the tensile strain energy density, 2aiei (ai, and ei are the major principal stress and strain, respectively), becomes equal to the material parameter, U0

1 a2

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