An extended finite element method with higher-order elements for curved cracks

Stazi, Furio Lorenzo; Budyn, Elisa; Chessa, John F; Belytschko, Ted

doi:10.1007/s00466-002-0391-2

Cited by 199 publications

(173 citation statements)

References 31 publications

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“…The expected optimal convergence rate for the error in the SIF using XFEM with topological enrichment is 0.5 [19,24,25,26,27].The first study presented here is the effect of the selection of the level set basis. The extraction domain radius is selected to be R = 0.2R c .…”

Section: Analysis Of Convergence Ratesmentioning

confidence: 95%

Convergence of domain integrals for stress intensity factor extraction in 2‐D curved cracks problems with the extended finite element method

González-Albuixech

Giner

Tarancón

et al. 2013

Numerical Meth Engineering

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WileyGonzález Albuixech, VF.; Giner Maravilla, E.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ.; Gravouil, A. (2013). Convergence of domain integrals for stress intensity factor extraction in 2-D curved cracks problems with the extended finite element method. International Journal for Numerical Methods in Engineering. 94(8):740-757. doi:10.1002/nme.4478. This is the peer reviewed version of the following article: Int. J. Numer. Meth. Engng 2013; 94:740-757, which has been published in final form at Wiley Online Library (wileyonlinelibrary.com SUMMARYThe aim of this study is the analysis of the convergence rates achieved with domain energy integrals for the computation of the stress intensity factors (SIF) when solving 2-D curved crack problems with the extended finite element method (XFEM). Domain integrals, specially the J-integral and the interaction integral, are widely used for SIF extraction and provide high accurate estimations with finite element methods. The crack description in XFEM is usually realized using level sets. This allows to define a local basis associated with the crack geometry. In this work the effect of the level set local basis definition on the domain integral has been studied. The usual definition of the interaction integral involves hypotheses that are not fulfilled in generic curved crack problems and we introduce some modifications to improve the behavior in curved crack analyses. Despite the good accuracy of domain integrals, convergence rates are not always optimal and convergence to the exact solution cannot be assured for curved cracks. The lack of convergence is associated with the effect of the curvature on the definition of the auxiliary extraction fields. With our modified integral proposal, the optimal convergence rate is achieved by controlling the q-function and the size of the extraction domain.

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Section: Analysis Of Convergence Ratesmentioning

confidence: 95%

Convergence of domain integrals for stress intensity factor extraction in 2‐D curved cracks problems with the extended finite element method

González-Albuixech

Giner

Tarancón

et al. 2013

Numerical Meth Engineering

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“…Linear tetrahedral elements are used to represent both the mechanical fields and the level set functions and therefore, the geometrical representation of the crack also is C 0 and piecewise linear. The method naturally extends to higher order shape functions [31,32].…”

Section: Discretized Equilibrium Equationsmentioning

confidence: 99%

Enriched finite elements and level sets for damage tolerance assessment of complex structures

Bordas

Moran

2006

Engineering Fracture Mechanics

153

116

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The extended finite element method (X-FEM) has recently emerged as an alternative to meshing/remeshing crack surfaces in computational fracture mechanics thanks to the concept of discontinuous and asymptotic partition of unity enrichment (PUM) of the standard finite element approximation spaces. Level set methods have been recently coupled with X-FEM to help track the crack geometry as it grows. However, little attention has been devoted to employing the X-FEM in real-world cases. This paper describes how X-FEM coupled with level set methods can be used to solve complex threedimensional industrial fracture mechanics problems through combination of an object-oriented (C++) research code and a commercial solid modeling/finite element package (EDS-PLM/I-DEAS Ò ). The paper briefly describes how object-oriented programming shows its advantages to efficiently implement the proposed methodology. Due to enrichment, the latter method allows for multiple crack growth scenarios to be analyzed with a minimal amount of remeshing. Additionally, the whole component contributes to the stiffness during the whole crack growth simulation. The use of level set methods permits the seamless merging of cracks with boundaries. To show the flexibility of the method, the latter is applied to damage tolerance analysis of a complex aircraft component.

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“…All of the examples to be presented use three node triangular elements. The implementation of quadrilaterals and higher-order elements is straightforward and does not introduce any difficulties in XFEM, see Stazi et al [30].…”

Section: Numerical Implementationmentioning

confidence: 99%

A new fast finite element method for dislocations based on interior discontinuities

Gracie

Ventura

Belytschko

2006

Numerical Meth Engineering

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SUMMARYA new technique for the modelling of multiple dislocations based on introducing interior discontinuities is presented. In contrast to existing methods, the superposition of infinite domain solutions is avoided; interior discontinuities are specified on the dislocation slip surfaces and the resulting boundary value problem is solved by a finite element method. The accuracy of the proposed method is verified and its efficiency for multi-dislocation problems is illustrated. Bounded core energies are incorporated into the method through regularization of the discontinuities at their edges. Though the method is applied to edge dislocations here, its extension to other types of dislocations is straightforward.

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An extended finite element method with higher-order elements for curved cracks

Cited by 199 publications

References 31 publications

Convergence of domain integrals for stress intensity factor extraction in 2‐D curved cracks problems with the extended finite element method

Convergence of domain integrals for stress intensity factor extraction in 2‐D curved cracks problems with the extended finite element method

Enriched finite elements and level sets for damage tolerance assessment of complex structures

A new fast finite element method for dislocations based on interior discontinuities

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