Meso-Scale Formulation of a Cracked-Hinge Model for Hybrid Fiber-Reinforced Cement Composites

This study presents a non-linear cracked-hinge model for the post-cracking response of fiber-reinforced cementitious composites loaded in bending. The proposed displacement-based model follows a meso-mechanical approach, which makes it possible to consider explicitly the random distribution and orientation of the reinforcing fibers. Moreover, the model allows for considering two different fiber typologies whereas the cement matrix is modelled as a homogeneous material. The proposed mechanical model combines a fracture-based, stress-crack opening relationship for the cementitious matrix with generalized laws aimed to capture the crack-bridging effect played by the reinforcing fibers. These laws are derived by considering both the fiber-to-matrix bond mechanism and fiber anchoring action possibly due to hooked ends. The paper includes a numerical implementation of the proposed theory, which is validated against experimental results dealing with fiber-reinforced cement composites reinforced with different short fibers. The excellent theory vs. experiment matching demonstrates the high technical potential of the presented model, obtained at a reasonable computational cost.