Arbitrary branched and intersecting cracks with the extended finite element method

Daux, Christophe; Moës, Nicolas; Dolbow, John E.; Sukumar, N.; Belytschko, Ted

doi:10.1002/1097-0207(20000830)48:12<1741::aid-nme956>3.0.co;2-l

Cited by 829 publications

(529 citation statements)

References 22 publications

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“…In the literature, numerical techniques such as the extended finite element method (X-FEM) [17,18], generalized finite element method [23], or the element partition method [24] are all particular instances of the partition of unity method. In the X-FEM, the emphasis has been on modeling discontinuities (such as cracks) with minimal enrichment.…”

Section: Extended Finite Element Methodsmentioning

confidence: 99%

“…Recently, there has been significant progress in the direction of discrete crack growth modeling -the development of a partition of unity finite element method for crack modeling (coined as the extended finite element method or X-FEM) [17,18] has provided an accurate and robust numerical method that removes the need to mesh the crack surfaces in static or quasi-static crack growth simula-N. SUKUMAR and D.J. SROLOVITZ 365 tions.…”

Section: Introductionmentioning

confidence: 99%

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Finite element-based model for crack propagation in polycrystalline materials

Sukumar

Srolovitz

2004

Mat. apl. comput.

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Abstract.In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.Mathematical subject classification: 74R10.

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Section: Extended Finite Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite element-based model for crack propagation in polycrystalline materials

Sukumar

Srolovitz

2004

Mat. apl. comput.

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“…The resolution of compressible fracture mechanics problems has been extensively studied in the context of the X-FEM for both 2D [39,18,40,32,24] and 3D fracture mechanics [21,22]. The most common enrichment strategy consists in using the asymptotic displacement field as an enrichment for the displacement finite element approximation.…”

Section: Incompressible Fracture Mechanicsmentioning

confidence: 99%

“…Proper enrichment of the finite element basis makes it possible to model crack, material inclusions and holes with non-conforming meshes. The X-FEM method has been used for the simulation of a wide variety of problems such as fracture mechanics problems (2D [18][19][20], 3D [21][22][23], plates [24,25], cohesive zone modeling [26,27], dynamic fracture [28], nonlinear fracture mechanics [29][30][31]), holes [32,33], but also material inclusions [33,34] or multiple phase flows [35]. Here, we focus on the application of this method to mixed formulations for the treatment of holes, material inclusions and cracks in the incompressible limit.…”

Section: Introductionmentioning

confidence: 99%

Stability of incompressible formulations enriched with X-FEM

Legrain

Moës

Huerta

2008

Computer Methods in Applied Mechanics and Engineering

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The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic flows occurs as in forming processes. The use of mixed finite element methods is known to prevent the locking of the finite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the finite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (X-FEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement field makes it possible to treat surfaces of discontinuity inside finite elements. In this paper, some strategies are proposed for the enrichment of mixed finite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the finite element convergence rate is preserved and the inf-sup condition is passed.

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“…Recently, the eXtended Stochastic Finite Element Method (X-SFEM) [5,6] has been proposed. This approach, which is an extension to the stochastic framework of the X-FEM method [7,8,9,10,11], relies on the implicit representation of complex geometries using random level-set functions and on the use of a Galerkin approximation at both stochastic and deterministic levels.…”

Section: Introductionmentioning

confidence: 99%

Identification of random shapes from images through polynomial chaos expansion of random level set functions

Stefanou

Nouy

Clément

2009

Numerical Meth Engineering

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To cite this version:G. Stefanou, Anthony Nouy, Alexandre Clement. Identification of random shapes from images through polynomial chaos expansion of random level-set functions. International Journal for Numerical Methods in Engineering, Wiley, 2009, 79 (2) SUMMARYIn this paper, an e cient method is proposed for the identi cation of random shapes in a form suitable for numerical simulation within the eXtended Stochastic Finite Element Method (X-SFEM).The method starts from a collection of images representing di erent outcomes of the random shape to identify. The key-point of the method is to represent the random geometry in an implicit manner using the level-set technique. In this context, the problem of random geometry identi cation is equivalent to the identi cation of a random level-set function, which is a random eld. This random eld is represented on a polynomial chaos basis and various e cient numerical strategies are proposed in order to identify the coe cients of its polynomial chaos decomposition. The performance of these strategies is evaluated through some "manufactured" problems and useful conclusions are provided. The propagation of geometrical uncertainties in structural analysis using the X-SFEM is nally examined.key words:Random geometry; Level-set method; Probabilistic identi cation; Polynomial chaos; Maximum likelihood; Extended stochastic nite element method.

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Arbitrary branched and intersecting cracks with the extended finite element method

Cited by 829 publications

References 22 publications

Finite element-based model for crack propagation in polycrystalline materials

Finite element-based model for crack propagation in polycrystalline materials

Stability of incompressible formulations enriched with X-FEM

Identification of random shapes from images through polynomial chaos expansion of random level set functions

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