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A mixed augmented Lagrangian‐extended finite element method for modelling elastic–plastic fatigue crack growth with unilateral contact
Author(s) -
Elguedj T.,
Gravouil A.,
Combescure A.
Publication year - 2007
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.2002
Subject(s) - finite element method , discretization , augmented lagrangian method , paris' law , lagrangian , structural engineering , extended finite element method , numerical analysis , mixed finite element method , mathematics , fracture mechanics , engineering , mathematical analysis , crack closure , mathematical optimization
The complete modelling of fatigue crack growth is still an industrial challenging issue for numerical methods. A new technique for the finite element modelling of elastic–plastic fatigue crack growth with unilateral contact on the crack faces is presented. The extended finite element method (X‐FEM) is used to discretize the equations, allowing for the modelling of arbitrary cracks whose geometries are independent of the finite element mesh. This paper presents an augmented Lagrangian formulation in the X‐FEM framework that is able to deal with elastic–plastic crack growth with treatment of contact. An original formulation, which takes advantages of two powerful numerical methods, is presented. Next the numerical issues such as contact treatment and numerical integration are addressed, and finally numerical examples are shown to validate the method. Copyright © 2007 John Wiley & Sons, Ltd.