Analysis of Cohesive Crack Growth by the Element-Free Galerkin Method

Soparat, Preecha; Nanakorn, Pruettha

doi:10.1017/s1727719100001544

Cited by 12 publications

(6 citation statements)

References 34 publications

(64 reference statements)

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“…Fracture modeling using numerical methods is well-developed following major advances in the past decade or two such as the extended finite element method (XFEM) and meshless methods [1][2][3][4][5][6][7][8][9][10][11]. These methods were proposed to eliminate the need of remeshing during crack propagation where the conventional finite element method finds difficulty.…”

Section: Introductionmentioning

confidence: 99%

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

Zhuang

Augarde

Mathisen

2012

Numerical Meth Engineering

301

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SUMMARY In 3D fracture modeling, the complexity of the evolving crack geometry during propagation raises challenges in stress analysis because the accuracy of results mainly relies on the accurate description of the crack geometry. In this paper, a numerical framework is developed for 3D fracture modeling where a meshless method, the element‐free Galerkin method, is used for stress analysis and level sets are used accurately to describe and capture crack evolution. In this framework, a simple and general formulation for associating the displacement jump in the field approximation with an arbitrary 3D curved crack surface is proposed. For accurate closure of the crack front, a tying procedure is extended to 3D from its original use in 2D in the previous paper by the authors. The benefits of level sets in improving the results accuracy and reducing the computational cost are explored, particularly in the model refinement and the confinement of the displacement jump. Issues arising in level sets updating are discussed and solutions proposed accordingly. The developed framework is validated with a number of 3D crack examples with reference solutions and shows strong potential for general 3D fracture modeling. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

Zhuang

Augarde

Mathisen

2012

Numerical Meth Engineering

301

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“…This study aims at developing an EFG‐based method that is able to effectively model not only 3D crack propagation, but also the crack surface interactions such as opening, closing and sliding, using a nonlinear contact iterative algorithm. It may be noted that contact algorithms have been employed for crack modelling using meshless methods by a few studies (e.g., ) but only for 2D problems. The rest of the paper is organized as follows: Section 2 briefly describes the fundamentals of the EFG method.…”

Section: Introductionmentioning

confidence: 99%

An element‐free Galerkin method for 3D crack propagation simulation under complicated stress conditions

Yang

2012

Numerical Meth Engineering

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SUMMARY This study develops an element‐free Galerkin method based on the moving least‐squares approximation to trace three‐dimensional crack propagation under complicated stress conditions. The crack surfaces are modelled by a collection of planar triangles that are added when cracks propagate. The visibility criterion is adopted to treat the screening effect of the cracks on the influenced domain of a Gaussian point. Cracks are assumed to propagate in the perpendicular planes at crack front points when the strain energy release rates reach the material fracture toughness. This method is unique in that it uses a nonlinear contact iterative algorithm to consider contributions of crack surface interaction to the global equilibrium equations, so that crack opening, sliding and closing under complicated stress states can be efficiently modelled. Two numerical examples of three‐dimensional quasi‐static crack propagation were modelled with satisfactory results. Copyright © 2012 John Wiley & Sons, Ltd.

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“…The CZM has been employed within a FEM, see, e.g., [54,55] and a BEM, see, e.g., [56] setting, also in conjunction with a partition of unity approach [47]. Furthermore, CZM has been introduced within a particle based approach as in the case of SPH [57], reproducing kernel particles [58], and the Element-Free Galerkin method [59].…”

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confidence: 99%

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

et al. 2019

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Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics (LEFM). The purpose of the study is to provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.

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Analysis of Cohesive Crack Growth by the Element-Free Galerkin Method

Cited by 12 publications

References 34 publications

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

An element‐free Galerkin method for 3D crack propagation simulation under complicated stress conditions

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

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