Coupling of discrete and smeared cracking models applied to reinforced concrete structures

Resumo

The nonlinearity inherent to concrete comes from the cracking process and the inelastic phenomena in the fracture process zone (FPZ). It is understood that initially, microcracks appear diffusely in the material medium, even under low-intensity loading conditions. In these initial stages, cracking develops stably, causing the structure's nonlinear response, which can still absorb loads. With the advancement of the process, the crack coalescence causes the significant growth of cracks so that a discontinuity in the material medium is observed. At this stage, propagation occurs in an unstable manner, and the structure loses the ability to absorb loads. In reinforced concrete, the manifestation of cracks occurs through multiple fronts due to the reinforcement steel that absorbs tensile forces and locally contains the crack propagation, which initially appears in regions not covered by the reinforcement steel. In more advanced stages, cracks can be observed that surpass the reinforcement steel region and propagate throughout the structure until its collapse. Over the years, two main approaches have stood out in the representation of concrete fracturing: smeared crack models and discrete crack models. Each model aims to represent the concrete response based on different hypotheses. In the smeared models, the medium is considered continuous, and the effects of cracking are represented by the elastic degradation of the material computed through constitutive models. In discrete models, the crack is represented by a material discontinuity inserted into the mesh. This work presents a strategy that combines smeared and discrete models applied to the modeling of flat reinforced concrete structures. The reinforcement steel will be represented by one-dimensional elements with elastoplastic behavior while maintaining the perfect bond between the steel rebar and concrete. In the representation of concrete fracturing, the FPZ will be represented by a scalar damage model for the continuous degradation of the material, and from a critical damage value, a discrete model, which considers multiple crack fronts, is activated by inserting a discontinuity into the mesh using a nodal duplication strategy, thus describing the final rupture process. Finally, numerical simulations will be presented to illustrate the model's performance.