An analytical approach to predict post-cracking behavior of steel fiber reinforced concrete considering the fibers orientation

The presence of steel fiber in plain concrete improves significantly the stiffness as well as the ductility of the material. However, themechanical behavior in the post-cracking stage of steel fiber-reinforced concrete depends on many factors. Among them, the orientation of the fibers is an important factor that is difficult to quantify. This paper presents a theoretical study that describes the fiber bridging mechanism under tensile stress using a closed-form analytical function. This proposed analytical model allows estimating the stress at a crack openingwhere the fiber orientation is represented by a Gaussian-like periodic distribution function. The relevance of the proposed model is validated through several numerical analyses with both pre-defined values of different material properties and geometrical parameters of the fibers and the experimental parameters of the two directtensile tests reported in the literature. The model shows an overall reasonable estimation and presents a lot ofpotential for further development.