Post-cracking constitutive model of UHPFRC incorporating fiber efficiency evolution: from experiments to numerical implementation

This study investigated the influence of steel fiber content on the post-cracking mechanical behavior of ultra-high-performance fiber-reinforced concrete (UHPFRC) and quantified the evolution of the macroscopic fiber efficiency factor η_e at different fiber contents. A systematic experimental program was conducted, including fiber pullout tests at different inclination angles and direct tensile and flexural tests on notched specimens with fiber contents ranging from 0% to 3%. The results showed that both the peak bridging stress and flexural strength increased with increasing fiber content, whereas η_e exhibited a non-monotonic trend. Specifically, η_e increased at low fiber contents but decreased at higher fiber contents, with a reduction of approximately 30.6% as the fiber content increased from 1% to 3%. Based on these results, a post-cracking constitutive model incorporating fiber bridging stress and matrix softening stress was developed. In this model, η_e was determined by inverse analysis to quantify the variation in fiber efficiency associated with coupled mechanisms, including the group effect, matrix spalling, and fiber-induced matrix confinement. The proposed model was implemented in LS-DYNA using a user-defined material subroutine (UMAT) within the framework of the fixed smeared crack model. The numerical simulations accurately reproduced the crack propagation process during fracture and showed good agreement with the experimental results. These findings demonstrate that the proposed model can effectively characterize the tensile softening and fracture behavior of UHPFRC under monotonic static loading while accounting for the evolution of fiber efficiency.