Stochastic Extension of NMMD Model for Fracture Behaviors of Concrete Materials

The non-linearity and randomness existing composite materials like concrete make it a challenging topic in safety analysis and reliability design of structures. In view of the unique capability of nonlocal macro-meso-scale consistent damage (NMMD) model in dealing with non-linearity of crack evolutions, the stochastic extension of NMMD model is proposed to analyze stochastic fracture behaviors of concrete materials. In this extended model, the stochastic harmonic function method of second kind is employed to characterize the spatial variability of concrete property. Numerical examples of three point bending beams without defect and with various sizes of initial crack demonstrate that the stochastic NMMD model is capable of not only capturing the uncertain fluctuations of peak load but also simulating the random walk of crack path with instantaneous transition of fracture modes as observed in experiments. Meanwhile, the effectiveness of stochastic NMMD model only assigned with a single random field (i.e., Young’s modulus) also implies the conventional assertion that stochastic simulations of quasi-brittle fracture should contain at least two mechanical properties with spatial randomness might be overly arbitrary. Last but not least, the investigation of fracture energy with stochastic fluctuations reveals that randomness as a result of heterogeneity would more-or-less improve the fracture toughness of concrete materials in the statistical sense.