Monte Carlo Simulation of Complex 2D Cohesive Fracture in Random Heterogeneous Quasi-Brittle Materials

This study develops a numerical method to simulate complex 2D crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. Cohesive interface elements with softening traction-separation laws are inserted into the initial mesh to model potential cracks. The softening laws are modelled by spatially-varying Weibull random fields. Extensive Monte Carlo simulations of a concrete specimen under uni-axial tension were carried out. It was found that increasing the variance of the tensile strength random fields with increased heterogeneity led to reduction in the mean peak load and increase in the standard deviation. The developed method provides a simple but effective tool for assessment of structural reliability.