Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: a 3D study

XT Su, James Yang, GH Liu

Research output: Contribution to journalArticle

Abstract

In a recent publication (Yang et al., 2009. Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials. Int. J. Solids Struct. 46 (17) 3222–3234), we developed a finite element method capable of modelling complex two-dimensional (2D) crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. The present study extends the method to model three-dimensional (3D) problems. First, 3D cohesive elements are inserted into the initial mesh of solid elements to model potential crack surfaces by a specially designed, flexible and efficient algorithm and corresponding computer program. The softening constitutive laws of the cohesive elements are modelled by spatially-varying 3D Weibull random fields. Monte Carlo simulations are then carried out to obtain statistical information of structural load-carrying capacity. A concrete cube under uniaxial tension was analysed as an example. It was found that as the 2D heterogeneous model, the 3D model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing heterogeneity in terms of the variance in the tensile strength random fields resulted in lower mean and higher standard deviation of peak loads. Due to constraint effects and larger areas of unsmooth, non-planar fracture surfaces, 3D modelling resulted in higher mean and lower standard deviation of peak loads than 2D modelling.
Original languageEnglish
Pages (from-to)2336-2345
Number of pages10
JournalInternational Journal of Solids and Structures
Volume47
Issue number17
Early online date6 May 2010
DOIs
Publication statusPublished - 15 Aug 2010
Externally publishedYes

Keywords

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

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