A meshless method with enriched weight functions for three‐dimensional crack propagation

Duflot, Marc

doi:10.1002/nme.1530

Cited by 89 publications

(63 citation statements)

References 56 publications

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“…In Reference [58], in the context of an adaptive moving least squares element free Galerkin method with extrinsic partition of unity enrichment, we present a possible explicit treatment of the crack geometry in quite complex settings including multiple cracks, initiation, growth and coalescence of arbitrary cracks in non-linear materials, statics and dynamics. Useful references for 3D crack growth in LEFM in the context of the EFG method are [51,52,53].…”

Section: Discussionmentioning

confidence: 99%

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An extended finite element library

Bordas

Nguyen

Dunant

et al. 2007

Numerical Meth Engineering

239

135

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SUMMARYThis paper presents and exercises a general structure for an object-oriented enriched finite element code. The programming environment provides a robust tool for extended finite element (XFEM) computations and a modular and extensible system. The program structure has been designed to meet all natural requirements for modularity, extensibility, and robustness. To facilitate meshgeometry interactions with hundreds of enrichment items, a mesh generator and mesh database are included. The salient features of the program are: flexibility in the integration schemes (subtriangles, subquadrilaterals, independent near-tip and discontinuous quadrature rules); domain integral methods for homogeneous and bi-material interface cracks arbitrarily oriented with respect to the mesh; geometry is described and updated by level sets, vector level sets or a standard method; standard and enriched approximations are independent; enrichment detection schemes: topological, geometrical, narrow-band, etc.; multi-material problem with an arbitrary number of interfaces and slip-interfaces; non-linear material models such as J2 plasticity with linear, isotropic and kinematic hardening. To illustrate the possible applications of our paradigm, we present two-dimensional linear elastic fracture mechanics for hundreds of cracks with local near-tip refinement, and crack propagation in two dimensions as well as complex three-dimensional industrial problems.

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Section: Discussionmentioning

confidence: 99%

“…The PUM may be applied in the context of meshfree methods such as the Element Free Galerkin method (EFG) [50,51,52,53], yielding enriched methods where crack tip fields [54], discontinuous derivatives [55] can be incorporated into the meshfree approximation. A recent overview of meshfree methods may be found in [56,57].…”

Section: Introductionmentioning

confidence: 99%

An extended finite element library

Bordas

Nguyen

Dunant

et al. 2007

Numerical Meth Engineering

239

135

View full text Add to dashboard Cite

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“…Moreover, the extension of the diffraction method into three dimensions is complex. Nevertheless, several authors have presented implementations of the diffraction method in 3D [216,217].…”

Section: The Diffraction Methodmentioning

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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“…Here, a smooth representation of the crack surface by level sets or non-uniform rational B-splines (NURBS) can definitely be advantageous. Another smooth-level set procedure is described by Duflot [19].…”

Section: Gauß Pointmentioning

confidence: 99%

“…The only articles (according to the knowledge of the authors) that describe the application of the element-free Galerkin method to three dimensional crack problems are the papers by Krysl and Belytschko [27]; Sukumar et al [49] and Duflot [19]. In all three papers, the visibility or the diffraction method was used to trace the crack.…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

2007

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This paper proposes a three dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modelled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results.Keywords extended element free Galerkin method (XEFG); three dimensional cracks; cohesive forces; static and dynamic fracture; extrinsic partition of unity enrichment; non-linear fracture mechanics.

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A meshless method with enriched weight functions for three‐dimensional crack propagation

Cited by 89 publications

References 56 publications

An extended finite element library

An extended finite element library

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

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

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