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

• Published in: International journal of solids and structures 2010-08, Vol.47 (17), p.2336-2345
• Main Authors: Su, X.T., Yang, Z.J., Liu, G.H.
• Format: Article
• Language: English
• Subjects: Cohesion; Cohesive elements; Computer simulation; Exact sciences and technology; Finite element method; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Mathematical models; Modelling; Monte Carlo methods; Monte Carlo simulation; Physics; Quasi-brittle materials; Random heterogeneous fracture; Solid mechanics; Structural and continuum mechanics; Three dimensional; Three-dimensional crack propagation; Two dimensional
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2010.04.031

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.