Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

Mohammad Malekan*, Felício B. Barros

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner–Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Original languageEnglish
JournalComputational Mechanics
Volume62
Issue number4
Pages (from-to)783-801
ISSN0178-7675
DOIs
Publication statusPublished - 1. Oct 2018
Externally publishedYes

Bibliographical note

Funding Information:
The first author (CNPq Scholarship, Brazil?Grant No. 151003/2017-3) and the other author gratefully acknowledge the important support of the Brazilian research agencies CNPq (National Council for Scientific and Technological Developments?Grant No. 308932/2016-1), CAPES (Coordination for the Improvement of Higher Education Personnel), and FAPEMIG (Foundation for Research Support of the State of Minas Gerais?Grant No. APQ-02460-16).

Funding Information:
Acknowledgements The first author (CNPq Scholarship, Brazil— Grant No. 151003/2017-3) and the other author gratefully acknowledge the important support of the Brazilian research agencies CNPq (National Council for Scientific and Technological Developments—Grant No. 308932/2016-1), CAPES (Coordination for the Improvement of Higher Education Personnel), and FAPEMIG (Foundation for Research Support of the State of Minas Gerais—Grant No. APQ-02460-16).

Keywords

  • Fracture mechanics
  • Generalized/extended FEM
  • Micro-defects
  • Stress intensity factor
  • Two-scale analysis

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