A phase-field regularized cohesive zone model for quasi-brittle materials with spatially varying fracture properties

This study develops a numerical method combining the phase-field regularized cohesive zone model (PF-CZM) and random fields for modeling of complicated mesoscopic fracture in quasibrittle materials. In this method, the material's fracture properties such as tensile strength and fracture energy are assumed as spatial random variables and represented by Weibull random fields (RFs), which are mapped to finite element meshes. The PF-CZM with cohesive softening laws are used to model quasi-brittle multi-crack initiation and propagation without remeshing. The new method is first validated by Monte Carlo simulations of a mesoscale concrete example under uniaxial tension, with the effects of correlation length and variance in RFs investigated. Two concrete beam examples, under mode-I and mixed-mode fracture respectively, are then successfully modelled. It is found that the developed method can predict realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. It provides an effective tool for calculation of structural reliability caused by materials' random heterogeneity.