Improved XFEM for multiple crack analysis: Accurate and efficient implementations for stress intensity factors

Wen, Liu; Tian, Rong; Wang, L.X.; Feng, Chun

doi:10.1016/j.cma.2023.116045

Cited by 19 publications

(5 citation statements)

References 72 publications

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“…The approach in [26] offers an efficient method to address problems involving two or more discontinuities within an enriched element; however, the splitting of the domain is necessary in order to obtain precise integration results. Similar integration approaches are also found in [27,28]. The proposed formulation fits well into this scope, delivering exact results through an efficient numerical integration algorithm without defining subdomains.…”

Section: Multiple Discontinuities Problemsmentioning

confidence: 69%

“…The integration algorithm presented in this paper, as well as the DD_EQP library implementing it, are helpful tools to evaluate the integral of multiple discontinuous functions by means of any numerical quadrature strategy, removing the need for dividing the domain of integration. The context for the proposed algorithm is mainly XFEM analysis of cracked bodies, in which scenarios involving crossing discontinuities are common [27,28,54,[78][79][80]. Moreover, as pointed out in Section 2, the existing methods for addressing multiple discontinuities problems make use of integration strategies in which partitioning of the domain is required.…”

Section: Discussionmentioning

confidence: 99%

“…Problems involving multiple discontinuities have been addressed by various authors [22,24,25,27,28,54,55]. A notable approach in the XFEM context has been proposed by Daux et al [26], in which a technique for modelling cracks with multiple branching is carried out.…”

Section: Multiple Discontinuities Problemsmentioning

confidence: 99%

“…The equivalent polynomials concept has been explored by the authors, and it has been extended to the case of a double discontinuity within a single finite element as a first step towards the integration of an arbitrary number of discontinuities. This situation is not uncommon and can be encountered when scenarios such as crack branching, kinking or junction occur [11,[21][22][23][24][25][26][27][28]. In this context, an efficient integration algorithm to exactly evaluate polynomials times double step function over quadrangular finite element domains is presented in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

et al. 2023

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The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable results. In this scope, equivalent polynomials represent an effective method to circumvent the problem while exploiting the standard Gauss quadrature rule to exactly integrate polynomials times step function. Certain scenarios, however, might require the integration of polynomials times two step functions (i.e., problems in which branching cracks, kinking cracks or crack junctions within a single finite element occur). In this context, the use of equivalent polynomials has been investigated by the authors, and an algorithm to exactly integrate arbitrary polynomials times two Heaviside step functions in quadrilateral domains has been developed and is presented in this paper. Moreover, the algorithm has also been implemented into a software library (DD_EQP) to prove its precision and effectiveness and also the proposed method’s ease of implementation into any existing computational software or framework. The presented algorithm is the first step towards the numerical integration of an arbitrary number of discontinuities in quadrilateral domains. Both the algorithm and the library have a wide application range, in addition to fracture mechanics, from mathematical computing of complex geometric regions, to computer graphics and computational mechanics.

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Section: Multiple Discontinuities Problemsmentioning

confidence: 69%

Section: Discussionmentioning

confidence: 99%

Section: Multiple Discontinuities Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

et al. 2023

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“…The method is not only available in commercial software such as Abaqus since version 6.9 (Simulia, Providence, RI, USA) and Ansys 17.2 (Canonsburg, PA, USA) but also in free software such as GetFEM 5.4.2 [32] and Code_Aster 14.6 [33]. Modifications of the XFEM have also been proposed [34][35][36][37][38][39].…”

Section: Availabilitymentioning

confidence: 99%

XFEM for Composites, Biological, and Bioinspired Materials: A Review

Vellwock,

Libonati

2024

Materials

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The eXtended finite element method (XFEM) is a powerful tool for structural mechanics, assisting engineers and designers in understanding how a material architecture responds to stresses and consequently assisting the creation of mechanically improved structures. The XFEM method has unraveled the extraordinary relationships between material topology and fracture behavior in biological and engineered materials, enhancing peculiar fracture toughening mechanisms, such as crack deflection and arrest. Despite its extensive use, a detailed revision of case studies involving XFEM with a focus on the applications rather than the method of numerical modeling is in great need. In this review, XFEM is introduced and briefly compared to other computational fracture models such as the contour integral method, virtual crack closing technique, cohesive zone model, and phase-field model, highlighting the pros and cons of the methods (e.g., numerical convergence, commercial software implementation, pre-set of crack parameters, and calculation speed). The use of XFEM in material design is demonstrated and discussed, focusing on presenting the current research on composites and biological and bioinspired materials, but also briefly introducing its application to other fields. This review concludes with a discussion of the XFEM drawbacks and provides an overview of the future perspectives of this method in applied material science research, such as the merging of XFEM and artificial intelligence techniques.

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Bond-based peridynamic fatigue analysis of ductile materials with Neuber’s plasticity correction

Altay,

Dorduncu,

Kadioglu

et al. 2024

Engineering with Computers

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Improved XFEM for multiple crack analysis: Accurate and efficient implementations for stress intensity factors

Cited by 19 publications

References 72 publications

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis

XFEM for Composites, Biological, and Bioinspired Materials: A Review

Bond-based peridynamic fatigue analysis of ductile materials with Neuber’s plasticity correction

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