New model for the analysis of size-scale effects on the ductility of reinforced concrete elements in bending

The well-known cohesive crack model describes strain localization with a softening stress variation in concrete members subjected to tension. An analogous behavior is also observed in compression, when strain localization takes place in a damaged zone and the stress reaches the compression strength with surface energy dissipation. In the present paper, we propose the new concept of overlapping crack model, which is analogous to the cohesive one and permits us to simulate material interpenetration due to crushing. The two aforementioned elementary models are merged into a more complex algorithm able to describe both cracking and crushing growths during loading processes in reinforced concrete members. A numerical procedure based on elastic coefficients is developed, taking into account the proposed constitutive laws in tension and compression. With this algorithm, it is possible to effectively capture the flexural behavior of reinforced concrete beams by varying the reinforcement percentage and/or the beam depth.