Softening behavior of reinforced concrete beams under cyclic loading

Aim of the paper is the study of the cyclic behavior of reinforced concrete beams taking into account the compression and tensile softening in the concrete material, the Baushinger effect in the steel and an adequate bond-slip law for the concrete-steel interface. Nonlinear material models are developed on the basis of damage mechanics and plasticity. In particular, an elastoplastic-damage model is developed for the concrete material introducing two damage variables, one in tension and one in compression. A plasticity model with nonlinear hardening is adopted for the reinforcing steel and a bond stress-slip law, suitable for cyclic behavior, is introduced for the concrete-steel interface. The governing equations are derived and a numerical procedure based on the arc-length method, within an implicit Euler algorithm for the time integration, is developed. Some numerical examples are carried out in order to analyze the axial and bending behavior of reinforced concrete beams under monotonic and cyclic loading. A comparison with experimental results available in literature is performed in order to validate the proposed model.