An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks

Wu, Jian‐Ying; Li, Fengbo

doi:10.1016/j.cma.2015.06.018

Cited by 102 publications

(54 citation statements)

References 67 publications

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“…The condition numbers obtained from the current computational results are compared with the condition numbers for the XFEM, as shown in Figure . Note that Wu and Li investigated the double‐edge‐notched specimen test using the XFEM. They used two types of meshes, and the numbers of elements are 594 and 1660, which lead to the approximated element sizes of 8 and 5 mm, respectively.…”

Section: Mixed‐mode Examplesmentioning

confidence: 99%

“…Furthermore, when the ratio of area (or volumes) on either side of the discontinuity in an element is very small, an ill‐conditioned system of equations for the GFEM/XFEM can be expected, which is associated with the accuracy and convergence of a problem . To improve conditioning and accuracy of the GFEM/XFEM, a preconditioning scheme was developed for a Heaviside enrichment function, whereas a stable GFEM/XFEM was proposed to solve fracture problems . Additionally, when a special enrichment function is utilized, the numerical integration should be performed with great caution .…”

Section: Introductionmentioning

confidence: 99%

“…19 To improve conditioning and accuracy of the GFEM/XFEM, a preconditioning scheme was developed for a Heaviside enrichment function, 20 whereas a stable GFEM/XFEM was proposed to solve fracture problems. [21][22][23] Additionally, when a special enrichment function is utilized, the numerical integration should be performed with great caution. 6,24 Recently, a phase-field model was also utilized for cohesive zone modeling, whereas fracture properties, such as fracture energy and cohesive strength, should be calibrated in conjunction with internal length-scale parameters, 25,26 and some form of numerical regularization was needed to prevent a loss of ellipticity.…”

Section: Introductionmentioning

confidence: 99%

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Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

Choi

Park

2019

Numerical Meth Engineering

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Summary To remove mesh bias and provide an accurate crack path representation in mixed‐mode investigation, a novel stress recovery technique is proposed in conjunction with a domain integral and element splits. Based on a domain integral and stress recovery technique, a maximum strain energy release rate is estimated to determine a crack path direction. Then, for a given crack path direction, continuum elements are split, and a cohesive surface element is adaptively inserted. One notes that the proposed stress recovery technique provides a more accurate stress field than a standard stress evaluation procedure. The proposed computational framework is verified and validated by solving mode‐I and mixed‐mode examples. Computational results demonstrate that the domain integral with the stress recovery accurately evaluates a crack path, even with a lower‐quality mesh and under a biaxial stress state. Furthermore, the cohesive surface element approach, with the element split in conjunction with the stress recovery and the domain integral, predicts mixed‐mode fracture behaviors while removing mesh bias in the crack path representation. Additionally, the condition numbers of stiffness matrices are within the same order of magnitude during cohesive fracture simulation.

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Section: Mixed‐mode Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

Choi

Park

2019

Numerical Meth Engineering

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“…However, the additional enrichment results in higher condition number of the stiffness matrix in comparison to the standard finite element approximation. To remedy the resulting poor conditioning, various approaches have been suggested in the literature, the review can be found in [8] . In the context of weak discontinuities, Hansbo et al [9] and Wadbro et al [10] improve the conditioning of the system by adding additional volume terms to the weak formulation of the problem.…”

Section: Introductionmentioning

confidence: 99%

An Improved XFEM for the Poisson Equation with Discontinuous Coefficients

Stąpór¹

2017

Archive of Mechanical Engineering

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AN IMPROVED XFEM FOR THE POISSON EQUATION WITH DISCONTINUOUS COEFFICIENTSDiscontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.

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“…For the past two decades, researchers have started to appreciate the use of numerical computations in solving numerous engineering problem [16]. It is commonly used to investigate the power plant [15], in automotives or aircraft [17,18] and for the fatigue life assessment [12,13,[19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Fatigue crack growth analysis on square prismatic with embedded cracks under tension loading

Shaari

Ariffin

Takahashi³

et al. 2017

J. MECH. ENG. SCI.

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One of the most important issues yet to be overcome by engineers is the integrity and reliability of engineering structures. This is to ensure the safety of the engineering structure is at the greatest since the catastrophic failures usually occur due to fatigue crack growth. Due to insufficient studies on the fatigue embedded crack growth, the prismatic bar is chosen as the model of the structure. It is wise to select the solid bar since the analysis can be much simpler, thus making it easier to examine the behaviour of the fatigue crack growth. In this study, the metallic square prismatic with embedded cracks is analysed using S-version Finite Element Modelling (S-version FEM) under tension loading. The S-version FEM is an open source program, that is built from codes previously compiled as a program. The S-version FEM structured using the global-local overlay technique consists of two separate global and local meshes. By using the basic concept from the energy release rate and stress intensity factors (SIF), the behaviour of the fatigue crack growth is analysed. From the linear elastic fracture mechanics concept, the SIF is calculated using the virtual crack closure-integral method. The influences of different initial crack size and aspect ratios on the fatigue crack growth are investigated in this study. In addition, the SIF results from the S-version FEM are compared with the analytical solutions. From the analysis, the root mean square errors (RMSE) are performed to support the validation. The RMSE shows a very small error of 0.227, 0.086 and 0.3089 according to the aspect ratio of 0.5, 1.0 and 2.0, respectively. The results also show significant characteristics and behaviour of the SIF trend along the crack front, corresponding to different aspect ratios. From this study, the S-version FEM is suitable to be used to predict the fatigue crack growth for the cracks embedded in a structure. Subsequently, the S-version FEM is an open source program can be modified for increasingly complex engineering problems.

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An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks

Cited by 102 publications

References 67 publications

Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

An Improved XFEM for the Poisson Equation with Discontinuous Coefficients

Fatigue crack growth analysis on square prismatic with embedded cracks under tension loading

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