Adaptive and Hierarchical Modeling of Fatigue Crack Propagation

Fish, Jacob; Nath, Aditya

doi:10.2514/6.1993-1504

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…In addition, some methods for an effective implementation of XFEM have been published in [18,19].An advantage of the XFEM scheme is that enrichments are local. This is not a feature unique to XFEM, but exists in other enrichment methods such as the embedded discontinuity model [20], the s-version FEM [21,22] and the spectral overlay method [23]. Recent works coupling the s-version FEM with partition of unity [24] based methods combine many of the advantages of the XFEM/GFEM and s-version schemes [25][26][27].In this work we will focus on two issues that arise in the XFEM.…”

mentioning

confidence: 99%

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

Ventura

Gracie

Belytschko

2008

Numerical Meth Engineering

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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mentioning

confidence: 99%

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

Ventura

Gracie

Belytschko

2008

Numerical Meth Engineering

181

141

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“…Due to the history dependence of crack growth, the problem of evaluating the amplitude can be stated in terms of an ordinary delay differential equation (Fish and Nath, 1993):…”

Section: Crack Propagation Proceduresmentioning

confidence: 99%

Automated Multiple-Scale Fracture Analysis

Fish¹,

Shephard²,

Beall³

et al. 2005

Int J Comp Civ Struct Eng

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Abstract. This paper discusses a system for automated analysis of crack propagation in heterogeneous materials. The system uses a multiscale analysis technique to account for the effect of the microstructure on the propagation of the crack. The multiscale analysis allows the microstructure of the composite to be explicitly represented in the vicinity of the crack front while using homogenized material properties elsewhere. Procedures for automatic construction and update of the models and meshes used in the analysis are described.

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Adaptive and Hierarchical Modeling of Fatigue Crack Propagation

Cited by 2 publications

References 9 publications

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

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

Automated Multiple-Scale Fracture Analysis

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