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A study of the representation of cracks with level sets
Author(s) -
Duflot Marc
Publication year - 2006
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.1915
Subject(s) - set (abstract data type) , computation , representation (politics) , displacement (psychology) , level set (data structures) , displacement field , plane (geometry) , fracture mechanics , level set method , mathematics , field (mathematics) , algorithm , geometry , computer science , structural engineering , engineering , finite element method , artificial intelligence , pure mathematics , image (mathematics) , psychology , politics , political science , law , image segmentation , psychotherapist , programming language
The level set method has been used for a few years to represent cracks in fracture mechanics simulations instead of an explicit description of the cracks faces geometry. This paper studies in detail the shape of the level set functions around a crack in two dimensions that is propagating with a sharp kink, obtained both with level set update methods found in the literature and with several innovative update methods developed by the author. A criterion based on the computation of a J integral of a virtual displacement field obtained with the values of the level set functions is proposed in order to assess the quality of these update methods. With the help of this criterion, two optimal approaches are identified, which predict an accurate evolution of the crack with smooth and consistent level set functions. These methods are then applied in three dimensions to the case of an initially penny‐shaped crack that propagates out of its plane. Copyright © 2006 John Wiley & Sons, Ltd.