A model for optimizing hooked end steel fibre reinforcements in cracked cement composites

The addition of metallic fibres in concrete is a widely used technique to increase its resistance to crack opening, energy absorption capacity, and durability. The properties of the resulting composite strongly depend on the geometry of the fibres, which usually dispose of an hooked end, as well as on the mechanical properties of both the fibre and the concrete. The optimization of the fibre reinforcement mechanisms can only be achieved by an approach that takes into account adequately these aspects. Therefore, in this work, a computational model incorporating the key features of a hooked end fibre embedded in a cement matrix is proposed. The fibre is modelled as a Timoshenko beam, whereas a cohesive interface is used to model the interaction with the surrounding concrete. Different failure mechanisms are defined including fibre debonding or fibre tensile rupture and concrete spalling at fibre exit point. The model is calibrated by using the results of an experimental campaign conducted by authors. A multi-step optimization algorithm is used to find the optimal geometry and model's constitutive parameters that maximize the peak pull-out force and the energy absorption capacity in a fibre pull-out test. The analysis suggests that the use of concrete with high strength has the potential to increase both peak force and energy absorption capacity by designing the proper geometry of the fibre.