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

Abstract

a b s t r a c tIn 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.

Experimental and numerical analysis of three-point bending fracture of pre-notched asphalt mixture beam

“…A lot of work has been done to investigate mesoscopic and microscopic characteristics of heterogeneous materials like cement concrete and a number of numerical heterogeneous models have been established in different ways [5][6][7][8][9][10]. As the most common ways, both the parameterization modeling method and the numerical image processing technique can be used to capture microstructural details in asphalt mixture.…”

Three‐Dimensional In Situ XCT Characterisation and FE Modelling of Cracking in Concrete

“…Figure 11 shows the generated mesh with 981,919 tetrahedrons using target minimum and maximum edge lengths of 0.1 mm and 0.5 mm. The cohesive interface element (CIE) COH3D6 in ABAQUS [32] with softening laws was inserted between all common faces of adjacent elements to model potential cracks using the algorithm developed in [1,33,34]. The solid elements for aggregates and cement were assumed linear elastic.…”

Local Monte Carlo Method for Fatigue Analysis of Coarse-Grained Metals with a Nanograined Surface Layer

“…Based on the scatter of concrete tensile strength and bond strength, Hartig and Häussler-Combe employed MCS to study the statistics of crack widths [30]. It is quite difficult for the MCS to deal with the high nonlinearity related to the fracture process because of the high computational cost associated with a large number of finite elements [31]. However, it is still an effective method to estimate the uncertainty of structural response.…”

“…However, it is still an effective method to estimate the uncertainty of structural response. So far, only limited studies have combined MCS with CFEM to study fracture behavior [31,32]. The MCS can be employed to study the fatigue failure process [33,34].…”

“…In Section 3, the effects of the random fields and loads on the fatigue life and damage evolution of both the CG and the SMATed specimens will be investigated. The main findings will be summarized in Section 4. study fracture behavior [31,32]. The MCS can be employed to study the fatigue failure process [33,34].…”