Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials

James Yang, XT Su, JF Chen, GH Liu

Research output: Contribution to journalArticlepeer-review

144 Citations (Scopus)


A 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 spatially-varying 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.

Original languageEnglish
Pages (from-to)3222-3234
Number of pages13
JournalInternational Journal of Solids and Structures
Issue number17
Early online date24 Apr 2009
Publication statusPublished - 15 Aug 2009
Externally publishedYes


  • Cohesive elements
  • Monte Carlo simulation
  • Finite element method
  • Random heterogeneous fracture
  • Quasi-brittle materials


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