Complete Generalization of the Equations for the Stress–Strain Curves of Concrete under Uniaxial Compression

Abstract

The existence of more than thirty stress–strain equations, including those proposed by the government regulations in many countries, seems to indicate that additional, unifying, and at the same time generalizing research is necessary for this subject. Many expressions can be found to set or determine the initial modulus of elasticity of concrete, i.e., the modulus of elasticity of concrete when no load has been applied to it. This work proposes a complete generalization of the equations based on scalar damage models, applicable to all types of concrete tested under uniaxial compression with any constant rate of stress or strain, although in no case can it be considered a constitutive model. We prefer to discuss an equation that models the shape of the stress–strain curve. Thus, the shape of this curve is studied here in the same way a forensic scientist would, which is why we could see this work as an autopsy carried out on the test specimen through the trace left in the plane σ-ε by the straining process up until its inevitable outcome. That is to say, we believe in a purely phenomenological approach. The results are compared with the data obtained experimentally by analyzing test specimens made using various mixed portions of cement, water, and aggregates.