Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes

Kim, Dae‐Jin; Pereira, J. P.; Duarte, C. Armando

doi:10.1002/nme.2690

Cited by 109 publications

(94 citation statements)

References 68 publications

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“…Dedicated strategies have been developed to handle these very different scales that are required to simulate cracked bodies. These methods can use energy coupling methods [3,13], domain decomposition methods [12,16], homogenization [8,10,1] or generalized FEM [17]. Among them a multiscale method has been recently proposed and adapted to X-FEM [27] which is based on a multigrid solver [5,25].…”

Section: Introductionmentioning

confidence: 99%

Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM

Passieux

Gravouil

Réthoré

et al. 2010

Numerical Meth Engineering

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mation of generalized stress intensity factors using a three-scale concurrent multigrid X-FEM. International Journal for Numerical Methods in Engineering, Wiley, 2011, 85 (13) Abstract A concurrent multigrid method is devised for the direct estimation of stress intensity factors (SIF) and higher order coefficients of the elastic crack tip asymptotic field. The proposed method bridges three characteristic length scales that can be present in fracture mechanics: the structure, the crack and the singularity at the crack tip. For each of them, a relevant model is proposed. First, a truncated analytical reduced order model based on the Williams' expansion is used to describe the singularity at the tip. Then, it is coupled with a standard X-FEM model which is known to be suitable for the scale of the crack. A multigrid solver finally bridges the scale of the crack to that of the structure for which a standard FE model is often accurate enough. Dedicated coupling algorithms are presented and the effects of their parameters are discussed. The efficiency and accuracy of this new approach is exemplifyed using three benchmarks.

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Section: Introductionmentioning

confidence: 99%

Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM

Passieux

Gravouil

Réthoré

et al. 2010

Numerical Meth Engineering

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show abstract

“…It is implemented by an object of the class GFemAssembler that was modified in order to transfer boundary condition from the global model to the several local models. A Cauchy boundary condition was implemented following Kim et al (2010) (here represented by Eq. (6)).…”

Section: Assembler Interfacementioning

confidence: 99%

“…Among the three aforementioned boundary conditions in section 4.6, according to Kim et al (2010), the Dirichlet boundary conditions (a limiting case of Cauchy boundary condition) lead to worse results than Cauchy boundary conditions. Thus, for all two examples, the Dirichlet boundary conditions are applied on the local problem boundaries in order to demonstrate the robustness of the methodology in the worst case scenario.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In the third step, the numerical integration for those global elements that contain local elements is done over the Gauss points of local elements, as proposed by Kim et al (2010). Consider that a global element contains n Le local elements and number of Gauss points for each local elements be equal to GP.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The great advantage is providing a well-refined description of the local problem. More information on global-local GFEM, considering its various aspects can be found in Duarte and Kim (2008), Kim et al (2008), Kim et al (2009), Kim et al (2010), Pereira et al (2011), Gupta et al (2012), Kim et al (2012), Gupta et al (2013), Evangelista et al (2013), Plews and Duarte (2015). According to Alves et al (2013), the similarity between GFEM/XFEM and FEM can allow a straightforward migration for these methods and also the reuse of the FEM structure.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Object-Oriented Class Organization for Global-Local Generalized Finite Element Method

Malekan

Barros

Pitangueira

et al. 2016

Lat. Am. j. solids struct.

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This paper shows and discusses a generic implementation of the global-local analysis toward generalized finite element method (GFEM gl ). This implementation, performed into an academic computational platform, follows the object-oriented approach presented by the authors in a previous work for the standard version of GFEM in which the shape functions of finite elements are hierarchically enriched by analytical functions, according to the problem behavior. In global-local GFEM, however, the enrichment functions are constructed numerically from the solution of a local problem. This strategy allows the use of a coarse mesh even when the problem produces complex stress distributions. On the other hand, a local problem is defined where the stress field presents high gradients and it is discretized using a large number of elements. The results of the local problem are used to enrich the global problem which improves the approximate solution. The great advantage is allowing a well-refined description of the local problem, when necessary, avoiding an overburden for the computation of the global solution. Details of the implementation are presented and important aspects of using this strategy are highlighted in the numerical examples.

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Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM

Zamani

Gracie

Eslami

2012

Numerical Meth Engineering

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SUMMARYA comprehensive study is performed on the use of higher-order terms of the crack tip asymptotic fields as enriching functions for the eXtended FEM (XFEM) for both cohesive and traction-free cracks. For tractionfree cracks, the Williams asymptotic field is used to obtain highly accurate stress intensity factors (SIFs), directly from the enriched degrees of freedom without any post-processing. The low accuracy of the results of the original research on this subject by Liu et al. [Int. J. Numer. Meth. Engng., 2004; 59:1103-1118 is remedied here by appropriate modifications of the enrichment scheme. The modifications are simple and can be easily included into an XFEM computer code. For cohesive cracks, the relevant asymptotic field is used, and two widely used criteria including the SIFs criterion and the stress criterion are examined for the crack growth simulation. Both linear and nonlinear cohesive laws are used. For the stress criterion, averaging is avoided due to the highly accurate crack tip approximation because of the higherorder enrichment. Then, a modified stress criterion is proposed, which is shown to be applicable to a wider class of problems. Several numerical examples, including straight and curved cracks, stationary and growing cracks, single and multiple cracks, and traction-free and cohesive cracks, are studied to investigate in detail the robustness and efficiency of the proposed enrichment scheme.

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Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes

Cited by 109 publications

References 68 publications

Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM

Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM

An Object-Oriented Class Organization for Global-Local Generalized Finite Element Method

Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM

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