SUMMARY An automatic crack propagation modelling technique using polygon elements is presented. A simple algorithm to generate a polygon mesh from a Delaunay triangulated mesh is implemented. The polygon element formulation is constructed from the scaled boundary finite element method (SBFEM), treating each polygon as a SBFEM subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks. Stress intensity factors are computed directly from their definitions without any nodal enrichment functions. An automatic remeshing algorithm capable of handling any n‐sided polygon is developed to accommodate crack propagation. The algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths. The efficiency of the polygon SBFEM in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack. Four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features. The predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature. Copyright © 2012 John Wiley & Sons, Ltd.

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a b s t r a c tA numerical method is developed to simulate complex two-dimensional crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. Potential cracks are represented by pre-inserted cohesive elements with tension and shear softening constitutive laws modelled by spatiallyvarying Weibull random fields. Monte Carlo simulations of a concrete specimen under uni-axial tension were carried out with extensive investigation of the effects of important numerical algorithms and material properties on numerical efficiency and stability, crack propagation processes and load-carrying capacities. It was found that the homogeneous model led to incorrect crack patterns and load-displacement curves with strong mesh-dependence, whereas the heterogeneous model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. 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 and calculation of characteristic material strength for structural design.