Stage model of stress-strain relationship for concrete under short-term load: Part 1: Ascending branch

Since the stress-strain diagram (SSD) indicates a number of distinct stages in the state of concrete, the stress-strain relationships cannot be encompassed within a single formula. It is shown that the peculiarities in the concrete behavior can be accounted for, if the widely-known fact of constancy of the instantaneous elastic modulus is taken to imply constancy of this modulus in general, the non-linearity being attributed to the atrophying effect of microcracking. It is shown that within the ascending branch of the SSD, the concrete under short-term load undergoes two stages: the elastic stage, and that of non-linear stress. For the first stage, the model is trivial; for the second, functions are derived describing the strain-dependence of the atrophying effect (hence, of the nominal stresses) — incorporating the elastic modulus, the peak strain and the elastic limit.

The presence of a Gaussian in the function of atrophy indicates stochasticity of the latter. In view of the constancy of the elastic modulus, and the impact of the atrophying effect on the live cross-section of the concrete, it follows that the specific stress and specific strength are a linear function of the strain right up to the strength point. A strength formula is also derived, relating the strength to the peak strain, the elastic limit and the initial elastic modulus.