A new model for monitoring nonlinear elastic behavior of reinforced concrete structures

To better approximate the actual behavior of reinforced concrete structures under static and monotonic loading, we consider the effect of shear, ductility, and the contribution of concrete in tension between two cracks, as well as the location and distribution of stresses and strains with their directions. Based on the model established by Smahi and Bouafia for concrete and its combination with the damage variable for steel (derived from the behavior law for strain-hardened steel), a homogenization law for composite structures has been proposed. The proposed model is essentially based on the theory of continuum mechanics (generalized Hooke’s law), the damage theory of irreversible processes applied to homogeneous and isotropic materials, and the analytical model established by Vecchio and Collins. The latter is applied to reinforced concrete structures in a plane stress state and is extended in this study to a tridirectional stress state. Taking into account the geometric percentage of steel, two independent damage variables (deviatoric and volumetric) have been used to influence the properties of the composite material in the nonlinear domain, and then a law of variation of Poisson’s ratio is proposed. A numerical finite element program has been developed and applied to slabs and beams “with and without stirrups” in three-point and four-point bending tests. The latter, based on secant stiffness, was compared with other existing software, allowing us to verify its performance in the simulation of reinforced concrete elements and to monitor the actual behavior of these structures, both theoretically and graphically, until failure.