2011
DOI: 10.1002/nme.3232
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Stabilized global-local X-FEM for 3D non-planar frictional crack using relevant meshes

Abstract: SUMMARYA stabilized global-local quasi-static contact algorithm for 3D non-planar frictional crack is presented in the X-FEM/level set framework. A three-field weak formulation is considered and allows an independent discretization of the bulk and the crack interface. Then, a fine discretization of the interface can be defined according to the possible complex contact state along the crack faces independently from the mesh in the bulk. Furthermore, an efficient stabilized non-linear LATIN solver dedicated to c… Show more

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Cited by 26 publications
(27 citation statements)
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References 40 publications
(100 reference statements)
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“…(1), (2), (3), (6) and (7) consist of the strong formulation of the crack model with contact and friction between the crack faces. As already shown in [10], an equivalent three field weak formulation (the global displacement field u, the local displacement field w and the Lagrange multipliers field k) at a given time t A ½0; T can be introduced (see [22]). …”
Section: The Three Field Weak Formulation Problem Statement and Globmentioning
confidence: 99%
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“…(1), (2), (3), (6) and (7) consist of the strong formulation of the crack model with contact and friction between the crack faces. As already shown in [10], an equivalent three field weak formulation (the global displacement field u, the local displacement field w and the Lagrange multipliers field k) at a given time t A ½0; T can be introduced (see [22]). …”
Section: The Three Field Weak Formulation Problem Statement and Globmentioning
confidence: 99%
“…(17) and (20)). We introduce a stabilization operator on the weak coupling condition between the global displacement field U and the interface displacement field W both on the left-hand side and the right-hand side of the linearized system (see [22] for proofs and implementation details). Eq.…”
Section: Nonlinear Stabilized X-fem For Frictional Cracksmentioning
confidence: 99%
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“…In these techniques the finite element spaces can be freely chosen at the price of adding new stabilizing terms to the formulation. Modifications of the Nitsche method have been applied to standard FEM [26,57,29,13], X-FEM [21,4,3] and interface problems [23,12,45,2,1]. Other techniques use different stabilized formulations.…”
Section: Introductionmentioning
confidence: 99%