A heterogeneous cohesive model for quasi-brittle materials considering spatially varying random fracture properties

Yang, Zhenjun; Xu, X. Frank

doi:10.1016/j.cma.2008.03.027

Cited by 104 publications

(70 citation statements)

References 46 publications

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“…concrete, geomaterials, composites) using non-Gaussian stochastic fields has been addressed by a large number of researchers e.g. [6,38,39,54,60,73,75,76,84,90,97,114,117,129,152,180,193]. As it is stated in a recent state-of-the-art article [75], a joint experimental-stochastic mechanics research is imperative in this area in order to validate the stochastic models and improve the safety and reliability of engineering material systems.…”

Section: Methods Extending the Translation Field Conceptmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

407

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a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.

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Section: Methods Extending the Translation Field Conceptmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

407

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“…The Weibull distribution function (Weibull 1939) is used to generate random distributions of the properties, as it has a simple structure and its applicability for modeling failure of brittle materials has been verified (Fang and Harrison 2002;Yang and Xu 2008;Gorjan and Ambrožič 2012). In this study, the fracture energy is considered as a random variable.…”

Section: Stochastic Approachmentioning

confidence: 99%

“…However, the applicability of the method is limited to the cases that a clear separation of scales exists and a closed-form macroscopic equation can be driven to describe the relevant microstructural details, e.g., morphology or constituent material properties (Geers et al 2010;Novák et al 2012). Spatially varying random field-based approaches are able to directly approximate the randomness through generation of spatial realizations of the properties associated with a given correlation structures, and the crack trajectory is modeled using FEM within the context of Monte Carlo simulation (Yang and Xu 2008;Stefanou 2009). …”

Section: Introductionmentioning

confidence: 99%

Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks During Brazilian Disk Test

et al. 2018

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Reliable prediction of fracture process in shale-gas rocks remains one of the most significant challenges for establishing sustained economic oil and gas production. This paper presents a modeling framework for simulation of crack propagation in heterogeneous shale rocks. The framework is on the basis of a variational approach, consistent with Griffith's theory. The modeling framework is used to reproduce the fracture propagation process in shale rock samples under standard Brazilian disk test conditions. Data collected from the experiments are employed to determine the testing specimens' tensile strength and fracture toughness. To incorporate the effects of shale formation heterogeneity in the simulation of crack paths, fracture properties of the specimens are defined as spatially random fields. A computational strategy on the basis of stochastic finite element theory is developed that allows to incorporate the effects of heterogeneity of shale rocks on the fracture evolution. A parametric study has been carried out to better understand how anisotropy and heterogeneity of the mechanical properties affect both direction of cracks and rock strength.

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“…A number of statistical realizations were studied using this method where random numbers were generated with different seeds. A similar distribution has been used by other researchers to introduce spatially non-uniform fracture energies in non-linear fracture mechanics problems, one of them being the work by Yang and Frank Xu [11]. The fracture energy scatter was introduced with a view to investigate the effect of varying the fracture energy (mode-I fracture energy in this case) on delamination initiation and propagation in a DCB specimen.…”

Section: Implementation Of Materials Variability In Cohesive Zone Modelmentioning

confidence: 99%

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

2013

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This raises the question of whether the inherent stochasticity of localised damage is of significance in terms of the global properties and design methods for such materials. This paper presents the numerical modelling based analysis of the effect of material randomness on delamination damage in CFRP materials by the implementation of stochastic cohesive-zone model (CZM) within the framework of the finite-element (FE) method. The initiation and propagation of delamination in a unidirectional CFRP double-cantilever beam (DCB) specimen loaded under mode-I was analyzed, accounting for the inherent microstructural stochasticity exhibited by such laminates via the stochastic CZM. Various statistical realizations for a half-scatter of 50% of fracture energy were performed, with probability a distribution based on Weibull's two-parameter probability density function. The damaged area and the crack lengths in laminates were analyzed, and the results showed higher values of those parameters for random realizations compared to the uniform case for the same levels of applied displacement. This indicates that deterministic analysis of composites using average properties may be non-conservative and a method based on probability may be more appropriate.

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A heterogeneous cohesive model for quasi-brittle materials considering spatially varying random fracture properties

Cited by 104 publications

References 46 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks During Brazilian Disk Test

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

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