Finite element modeling of dynamic fracture in concrete through the initial fracture toughness-based criterion and field variable transference technique

Objective of the present study is to model the mode I dynamic crack propagation of concrete three-point bending (TPB) beams by using an initial fracture toughness-based criterion, and to evaluate the contribution of the rate and the inertia effects to the dynamic responses of concrete beams during crack growth. Firstly, the theory and implementation of the initial fracture toughness-based criterion are described in detail. Specifically, a field variable transference (FVT) technique is introduced to realistically reflect the coupling effect of the moving cracks and stress waves. Then, analysis procedures for static and dynamic crack growth are established. The comparison between the simulated and experimental impact and reaction forces indicates that, the initial fracture toughness-based criterion can accurately predict the mode I dynamic crack extension in concrete TPB beams. Moreover, the effects of the inertia and rate effects on dynamic responses (i.e., load, deformation, crack propagation velocity, and energy evolution and partition) are evaluated by performing numerical experiments on the mode I crack growth of TPB beams under a wide range of loading rates from 0.0002 mm/s to 2000 mm/s. It is concluded that, for the adopted concrete TPB beams, the inertia effect can be neglected and only the rate effect needs to be taken into account if the loading rate does not exceed 2 mm/s. Otherwise, if the loading rate exceeds 500 mm/s, only the inertia effect needs to be considered. In addition, the effect of damping on dynamic responses is investigated, and it is found that the damping effect can be ignored at high loading rates.