2010
DOI: 10.1002/nme.2914
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Abstract: Abstract.The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along wit… Show more

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Cited by 1,121 publications
(666 citation statements)
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References 239 publications
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“…Please note that there is no partial enrichment, i.e. the complete domain is enriched so that no blending [3] is necessary. For the integrals which are evaluated at the boundary and include enrichment functions, we use a numerical high order Gauß integration scheme.…”
Section: Square-based Homogeneous Isotropic Pyramid With Crackmentioning
confidence: 99%
See 1 more Smart Citation
“…Please note that there is no partial enrichment, i.e. the complete domain is enriched so that no blending [3] is necessary. For the integrals which are evaluated at the boundary and include enrichment functions, we use a numerical high order Gauß integration scheme.…”
Section: Square-based Homogeneous Isotropic Pyramid With Crackmentioning
confidence: 99%
“…As a remedy, we propose the use of enriched base functions on the discretized boundary. This enrichment approach, also known from the popular eXtended Finite Element Method [3], is applied to the SBFEM displacement representation.…”
Section: Introductionmentioning
confidence: 99%
“…Examples of such alternative methods include the diffuse element or element-free Galerkin methods [9,10], least-squares FEM [11], generalized or meshless finite different methods [12,13,14,15,16], generalized or extended FEM [17,18], and partition-of-unity FEM [19]. To reduce the dependency on mesh quality, these methods avoid the use of the piecewise-polynomial Lagrange basis functions found in the classical FEM.…”
Section: Introductionmentioning
confidence: 99%
“…The extended finite element method (XFEM) has developed to be a well-accepted and promising tool for the simulation of cracks [1,2]. The method features the consideration of inner-element discontinuities and singularities by adding customtailored enrichments to the classical finite element approximation space.…”
Section: Introductionmentioning
confidence: 99%
“…Recent developments in the field of the XFEM are discussed in the special issue in [3]. A recent overview on the XFEM is given in [2].…”
Section: Introductionmentioning
confidence: 99%