A two-scale stochastic damage model for concrete under fatigue loading

The microscopic stochastic fracture model is extended by introducing a concept of microscale damage, whose evolution law is derived by an energy analysis on the propagation of the cracks from nano- to microscale. A material parameter termed nano-to-micro comprehensive fracture energy is found to play a key role in the random and nonlinear behavior of concrete. It is shown that the proposed model can simulate the mean and standard deviation of the complete stress-strain curve of concrete very well. Moreover, the fatigue life, stiffness degradation and their inherent randomness under various loading conditions can be well predicted by the model.