A creep damage model for cracked concrete accounting for the rate of crack opening in a discrete strong discontinuity framework

Experimental studies have shown that viscoelastic creep effects significantly impact the post-cracking behaviour of quasi-brittle materials, making it crucial to consider these within the fracture process zones. This paper presents a discrete crack finite element approach that accounts for the rate of crack opening in discrete crack models by using a separation of variables. A time-dependent discrete strong discontinuity approach is first developed using a static damage model and is then extended to handle rate-dependent loading conditions common in viscoelastic models. Constitutive model parameters are defined based on the creep-induced changes in the fracture process zone, which are correlated with the behaviour of the rheologic model outside the fracture zone. The proposed model is assessed against experimental data and validated through several benchmark examples with load ratios ranging from 36% to 92% of the maximum load capacity, considering the ability to predict size effects and rupture failure, while reproducing the time-dependent behaviour of the concrete members. Additionally, the model successfully captures the transitions between instantaneous and time-dependent analyses. The results confirm that the proposed framework can provide reliable predictions for the behaviour of concrete structures under time-dependent conditions within the context of discrete crack models.