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Adaptive strategies and error control for computing material forces in fracture mechanics
Author(s) -
Heintz Per,
Larsson Fredrik,
Hansbo Peter,
Runesson Kenneth
Publication year - 2004
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.1007
Subject(s) - discretization , fracture (geology) , fracture mechanics , cauchy stress tensor , stiffness , mathematics , tangent , tensor (intrinsic definition) , tangent stiffness matrix , dual (grammatical number) , mathematical analysis , stiffness matrix , geometry , structural engineering , engineering , art , geotechnical engineering , literature
The concept of material forces pertains to a variation of the inverse motion map while the placement field is kept fixed. From the weak formulation of the self‐equilibrating Eshelby (material) stress tensor it turns out that the classical J‐integral formulations in fracture mechanics are just special cases due to the choice of particular weight functions. In this contribution, we discuss a posteriori error control of the material forces as part of an adaptive strategy to reduce the discretization error to an acceptable level. The data of the dual problem involves the quite non‐conventional tangent stiffness of the (material) Eshelby stress tensor with respect to a variation of the (physical) strain field. The suggested strategy is applied to the common fracture mechanics problem of a single‐edged crack, whereby different strategies for computing the J‐integral are compared. We also consider the case in which the crack edges are not parallel, i.e. a notch. Copyright © 2004 John Wiley & Sons, Ltd.