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Coarse‐graining of multiscale crack propagation
Author(s) -
Belytschko Ted,
Song JeongHoon
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2694
Subject(s) - discontinuity (linguistics) , hourglass , granularity , stiffness , materials science , nucleation , mechanics , finite element method , discrete element method , fracture mechanics , structural engineering , mathematics , composite material , computer science , mathematical analysis , physics , engineering , thermodynamics , astronomy , operating system
A method for coarse graining of microcrack growth to the macroscale through the multiscale aggregating discontinuity (MAD) method is further developed. Three new features are: (1) methods for treating nucleating cracks, (2) the linking of the micro unit cell with the macroelement by the hourglass mode, and (3) methods for recovering macrocracks with variable crack opening. Unlike in the original MAD method, ellipticity is not retained at the macroscale in the bulk material, but we show that the element stiffness of the bulk material is positive definite. Several examples with comparisons with direct numerical simulations are given to demonstrate the effectiveness of the method. Copyright © 2009 John Wiley & Sons, Ltd.