A finite element method with mesh-separation-based approximation technique and its application in modeling crack propagation with adaptive mesh refinement

Daosheng Ling, Lingfang Bu, Fubin Tu, Qingda Yang, Yunmin Chen

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

This paper presents a FEM with mesh-separation-based approximation technique that separates a standard element into three geometrically independent elements. A dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation. The novel technique makes it very easy for mesh generation of problems with complex or solution-dependent, varying geometry. It offers a flexible way to construct displacement approximations and provides a unified framework for the FEM to enjoy some of the key advantages of the Hansbo and Hansbo method, the meshfree methods, the semi-analytical FEMs, and the smoothed FEM. For problems with evolving discontinuities, the method enables the devising of an efficient crack-tip adaptive mesh refinement strategy to improve the accuracy of crack-tip fields. Both the discontinuities due to intra-element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level. The effectiveness and robustness of the present method are benchmarked with several numerical examples. The numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test, and it is essential to apply local adaptive mesh refinement for low fracture energy problems.

Original languageEnglish (US)
Pages (from-to)487-521
Number of pages35
JournalInternational Journal for Numerical Methods in Engineering
Volume99
Issue number7
DOIs
StatePublished - Aug 17 2014

Keywords

  • Adaptive mesh refinement
  • Approximation technique
  • Discontinuity
  • FEM
  • Hanging node

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

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