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

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 u...

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Vydáno v:Computational mechanics Ročník 62; číslo 4; s. 783 - 801
Hlavní autoři: Malekan, Mohammad, Barros, Felício B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2018
Springer Nature B.V
Témata:
Classical and Continuum Physics
Computational Science and Engineering
Computer simulation
Defects
Engineering
Enrichment
Finite element analysis
Finite element method
Fracture mechanics
Inhomogeneity
Linear elastic fracture mechanics
Mathematical models
Mindlin plates
Nonlinear programming
Numerical analysis
Original Paper
Plane stress
Theoretical and Applied Mechanics
Micro-defects
Fracture mechanics
Stress intensity factor
Generalized/extended FEM
Two-scale analysis
ISSN:0178-7675, 1432-0924
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Shrnutí: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.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-017-1527-8