A probabilistic semi-explicit model for crack propagation in concrete structures under dynamic loading

In this paper, concrete cracking is investigated in dynamics through finite element modeling. A probabilistic approach is employed to translate the effects of material heterogeneity on tensile strength and fracture energy. Both parameters depend on compressive strength and heterogeneity degree (volumetric ratio between finite element and largest aggregate). Material softening is modeled through damage theory. The actual concrete strengthening effect is modeled by an empirical formulation and similar reasoning is adopted for fracture energy. The apparent strengthening effect is naturally captured when mass and damping are included in the equation of motion. A convergence test is shown, indicating the probabilistic model proposed here is mesh-insensitive, converging in the average sense when both finite element size and load/time increment decrease. Then, experimental data are selected from literature for a wide range of loading rates. The effect of strain rate on the dispersion of crack pattern, load-carrying capacity and load–displacement curve is discussed. The influence of structural damping on the shape of load–displacement curve is also remarked.