Hanging nodes and XFEM

Fries, Thomas‐Peter; Byfut, A.; Alizada, A. N.; Cheng, Kwok Wah; Schröder, Jörg

doi:10.1002/nme.3024

Cited by 84 publications

(52 citation statements)

References 52 publications

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“…Moreover, adaptive hrefinement can be easily implemented in a meshfree context [185][186][187]. Though all methods discussed so far are capable of capturing discrete cracks, a certain refinement around the crack front is still needed for accuracy and efficiency reasons [188]. The meshfree approximation is similar to the FEM formulation:…”

Section: Meshfree Methodsmentioning

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

162

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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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Section: Meshfree Methodsmentioning

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

162

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“…An alternative idea suggested by [33,34] is to enhance the coarse elements with suitable shape modes, which recover the C 0 continuity between interconnected elements. Although this idea is very appealing and leads to optimal convergence, it has the disadvantage that an extension to high-order shape functions is not straightforward.…”

Section: Classical Refinement Schemesmentioning

confidence: 99%

Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes

et al. 2015

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The implementation of hp-adaptivity is challenging as hanging nodes, edges, and faces have to be constrained to ensure compatibility of the shape functions. For this reason, most hp-code frameworks restrict themselves to 1-irregular meshes to ease the implementational effort. This work alleviates these difficulties by introducing a new formulation for high-order mesh adaptivity that provides full local hp-refinement capabilities at a comparably small implementational effort. Its main idea is the extension of the hp-d-method such that it allows for high-order overlay meshes yielding a hierarchical, multi-level hp-formulation of the Finite Element Method. This concept enables intuitive refinement and coarsening procedures, while linear independence and compatibility of the shape functions are guaranteed by construction. The proposed method is demonstrated to achieve exponential rates of convergence-both in terms of degrees of freedom and in run-time-for problems with nonsmooth solutions. Furthermore, the scheme is used alongside the Finite Cell Method to simulate the heat flow around moving objects on a non-conforming background mesh and is combined with an energy-based refinement indicator for automatic hp-adaptivity.

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“…Fries et al [20] reported two approaches to adapt quadtree meshes into the extended finite element method. The first approach uses the transition elements developed by Gupta [14].…”

Section: Introductionmentioning

confidence: 99%

Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling

Ooi

Man

Natarajan

et al. 2015

Engineering Fracture Mechanics

121

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A crack propagation modelling technique combining the scaled boundary finite element method and quadtree meshes is developed. This technique automatically satisfies the compatibility requirement between adjacent quadtree cells irrespective of the presence of hanging nodes. The quadtree structure facilitates efficient data storage and rapid computations. Only a single cell is required to accurately model the stress field near crack tips. Crack growth is modelled by splitting the cells in the mesh into two. The resulting polygons are directly modelled by the scaled boundary formulation with minimal changes to the mesh. Four numerical examples demonstrate the salient features of the technique.

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Hanging nodes and XFEM

Cited by 84 publications

References 52 publications

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

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

Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes

Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling

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