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

Abstract

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.

Finite Element Analysis of Concrete Beam under Flexural Stresses Using Meso-Scale Model

“…İt can be satisfied by the maximum hoop stress and the principle stress criteria introduced by Erdogan [8]. In this study, the maximum principle stress was adopted for the crack initiation and evolution as shown in material properties (section 2).…”

“…On the other hand, the indirect method dose not comprise the modeling of concrete multi phases explicitly. Furthermore, the heterogeneity of concrete may be modeled separately with a regular FE mesh Yang [8], or by using lattice modeling for the aggregate and mortar phases Leiti [9], and Schlangen [10]. In this study the direct method will be employed for the modeling and analysis.…”

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

“…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].…”

Three-Dimensional Analysis of the Effect of Material Randomness on the Damage Behaviour of CFRP Laminates with Stochastic Cohesive-Zone Elements

“…A further contribution by Silberschmidt [5] presented a lattice model which was used to study damage and fracture evolution in laminates, linking microstructural randomness with macroscopic properties and demonstrating that a random character in the fibres' distribution results in fluctuations of local elastic moduli, the bounds of which depend on the characteristic length scale. Yanga et al [6] simulated two-dimensional crack propagation in quasi-brittle materials considering both uniform and randomly variable fracture properties. They concluded that the use of the homogeneous model leads to erroneous predictions of crack patterns and load-displacement curves whereas the models where the variable fracture properties were taken into account, presented a more realistic representation.…”