Failure Evaluation of Reinforced Concrete Beams Using Damage Mechanics and Classical Laminate Theory

The prediction of the behavior of reinforced concrete beams under bending is essential for the perfect design of these elements. Usually, the classical models do not incorporate the physical nonlinear behavior of concrete under tension and compression, which can underestimate the deformations in the structural element under short and long-term loads. In the present work, a variational formulation based on the Finite Element Method is presented to predict the flexural behavior of reinforced concrete beams. The physical nonlinearity due cracking of concrete is considered by utilization of damage concept in the definition of constitutive models, and the lamination theory it is used in discretization of section cross of beams. In the layered approach, the reinforced concrete element is formulated as a laminated composite that consists of thin layers, of concrete or steel that has been modeled as elasticperfectly plastic material. The comparison of numerical load-displacement results with experimental results found in the literature demonstrates a good approximation of the model and validates the application of the damage model in the Classical Laminate Theory to predict mechanical failure of reinforced concrete beam. The results obtained by the numerical model indicated a variation in the stress–strain behavior of each beam, while for under-reinforced beams, the compressive stresses did not reach the peak stress but the stress–strain behavior was observed in the nonlinear regime at failure, for the other beams, the concrete had reached its ultimate strain, and the beam’s neutral axis was close to the centroid of the cross-section