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Smooth Generalized/eXtended FEM approximations in the computation of configurational forces in linear elastic fracture mechanics

Authors
  • Torres, Diego Amadeu F.1
  • de Barcellos, Clovis S.2
  • Mendonça, Paulo de Tarso R.2
  • 1 Federal University of Technology of Paraná - UTFPR, Department of Mechanical Engineering, Londrina, PR, 86036-370, Brazil , Londrina (Brazil)
  • 2 Federal University of Santa Catarina - UFSC, Group of Mechanical Analysis and Design, Department of Mechanical Engineering, Florianópolis, SC, 88040-900, Brazil , Florianópolis (Brazil)
Type
Published Article
Journal
International Journal of Fracture
Publisher
Springer Netherlands
Publication Date
Feb 23, 2019
Volume
216
Issue
2
Pages
185–210
Identifiers
DOI: 10.1007/s10704-019-00353-1
Source
Springer Nature
Keywords
License
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Abstract

The computation of crack severity parameters in the linear elastic fracture mechanics (LEFM) modeling is strongly dependent on the local quality of the approximated stress fields right at the crack tip vicinity. This work investigates the behavior of extrinsically enriched smooth mesh-based approximations, obtained via Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{k}$$\end{document}-GFEM framework (Duarte et al. in Comput Methods Appl Mech Eng 196:33–56, 2006), in the computation of J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {J}$$\end{document}-integral in both pure mode I and mixed-mode loadings for two-dimensional problems of the LEFM. The method of configurational forces is used for this purpose as shown in Steinmann et al. (Int J Solids Struct 38:5509–5526, 2001), for instance, by performing some adaptations according to Häusler et al. (Int J Numer Methods Eng 85:1522–1542, 2011). As such method provides vector quantities, it is also possible to compute the angle θADV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _{{\mathrm{ADV}}}$$\end{document} of probable crack advance. The Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{k}$$\end{document}-GFEM is quite versatile and shares similar features with the standard FEM regarding the domain partition and numerical integration (Mendonça et al. in Finite Elem Anal Des 47:698–717, 2011). The tests were conducted using three-noded triangular element meshes and numerical integrations were performed using only global coordinates. The evaluations combined different schemes of polynomial and discontinuous/singular (Moës et al. in Int J Numer Methods Eng 46:131–150, 1999) enrichments. The use of a smooth partition of unity (PoU) can influence the accuracy of computed crack severity parameters. The configurational forces computation is favored by the smoothness, reducing the dependence on the way the crack severity parameters are evaluated.

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