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

Gracie, Robert; Ventura, Giulio; Belytschko, Ted

doi:10.1002/nme.1896

Cited by 77 publications

(61 citation statements)

References 35 publications

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“…This problem can be posed as the analysis of a body containing an embedded surface of discontinuity where the relative displacements (or jump in displacements) across the surface of discontinuity are prescribed according to the Burgers vector b of the dislocation. XFEM has been applied to the mesoscale modeling of dislocations in two dimensions [109,50,12,49], three dimensions [49,82] and in thin shells such as carbon nanotubes [82].…”

Section: Dislocationsmentioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

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1,178

695

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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 with the history of developments.

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Section: Dislocationsmentioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

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1,178

695

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“…Nevertheless, fine-scale features can also be incorporated "hierarchically" through enrichment. For example, Gracie et al [321,322], Belytschko and Gracie [323] developed special enrichment functions for dislocations.…”

Section: Isrn Applied Mathematicsmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

161

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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“…S ∞ is the set of nodes within a given number of element layers from the glide plane or core, as shown in Figure 6(a). is defined by (17), where d i and d e are defined to be constant distances from the glide plane, as shown in Figure 13(a). We label this enrichment EEL because it corresponds to the enriched element layers scheme used in [8] with the standard XFEM.…”

Section: Singular Enrichment Without Heaviside Enrichment and With A mentioning

confidence: 99%

Fast integration and weight function blending in the extended finite element method

Ventura

Gracie

Belytschko

2008

Numerical Meth Engineering

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181

141

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SUMMARYTwo issues in the extended finite element method (XFEM) are addressed: efficient numerical integration of the weak form when the enrichment function is self-equilibrating and blending of the enrichment. The integration is based on transforming the domain integrals in the weak form into equivalent contour integrals. It is shown that the contour form is computationally more efficient than the domain form, especially when the enrichment function is singular and/or discontinuous. A method for alleviating the errors in the blending elements is also studied. In this method, the enrichment function is pre-multiplied by a smooth weight function with compact support to allow for a completely smooth transition between enriched and unenriched subdomains. A method for blending step function enrichment with singular enrichments is described. It is also shown that if the enrichment is not shifted properly, the weighted enrichment is equivalent to the standard enrichment. An edge dislocation and a crack problem are used to benchmark the technique; the influence of the variables that parameterize the weight function is analyzed. The resulting method shows both improved accuracy and optimum convergence rates and is easily implemented into existing XFEM codes.

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

Cited by 77 publications

References 35 publications

The extended/generalized finite element method: An overview of the method and its applications

The extended/generalized finite element method: An overview of the method and its applications

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Fast integration and weight function blending in the extended finite element method

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