Premium
Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM
Author(s) -
Passieux J. C.,
Gravouil A.,
Réthoré J.,
Baietto M. C.
Publication year - 2010
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.3037
Subject(s) - singularity , stress intensity factor , multigrid method , finite element method , solver , fracture mechanics , scale (ratio) , structural engineering , coupling (piping) , mathematics , stress (linguistics) , computer science , mathematical analysis , engineering , mathematical optimization , physics , partial differential equation , mechanical engineering , linguistics , philosophy , quantum mechanics
A concurrent multigrid method is devised for the direct estimation of stress intensity factors and higher‐order coefficients of the elastic crack tip asymptotic field. The proposed method bridges three characteristic length scales that can be present in fracture mechanics: the structure, the crack and the singularity at the crack tip. For each of them, a relevant model is proposed. First, a truncated analytical reduced‐order model based on Williams' expansion is used to describe the singularity at the tip. Then, it is coupled with a standard extended finite element (FE) method model which is known to be suitable for the scale of the crack. A multigrid solver finally bridges the scale of the crack to that of the structure for which a standard FE model is often accurate enough. Dedicated coupling algorithms are presented and the effects of their parameters are discussed. The efficiency and accuracy of this new approach are exemplified using three benchmarks. Copyright © 2010 John Wiley & Sons, Ltd.