A two-scale extended finite element method for modelling 3D crack growth with interfacial contact

Pierres, Emilien; Baietto, Marie-Christine; Gravouil, Anthony

doi:10.1016/j.cma.2009.12.006

Cited by 38 publications

(43 citation statements)

References 30 publications

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“…The fictitious domain approach we consider in this work is the one using "cut elements" which is currently a subject of growing interest and is closely related to XFem approach introduced in [21] and widely studied since then (see for instance [20,16,26,4,23]). The case of a body with a Dirichlet (or transmission) condition with the use of cut-elements is studied in [16] when Lagrange multipliers and a Barbosa-Hughes stabilization are used, and in [14,4,1] when Nitsche's method and an additional interior penalty stabilization are considered.…”

Section: Fabre J Pousin Et Almentioning

confidence: 99%

A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method

Fabre

Pousin

Renard³

2016

The SMAI Journal of Computational Mathematics

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Abstract. In this paper, we develop and analyze a finite element fictitious domain approach based on Nitsche's method for the approximation of frictionless contact problems of two deformable elastic bodies. In the proposed method, the geometry of the bodies and the boundary conditions, including the contact condition between the two bodies, are described independently of the mesh of the fictitious domain. We prove that the optimal convergence is preserved. Numerical experiments are provided which confirm the correct behavior of the proposed method.Math. classification. 65N85, 35M85, 74M15.

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Section: Fabre J Pousin Et Almentioning

confidence: 99%

A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method

Fabre

Pousin

Renard³

2016

The SMAI Journal of Computational Mathematics

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“…More recent methods aimed at crack growth modeling and based on multiscale concepts include the multigrid methods proposed in [45,50]; the method of Guidault et al [26] based on the LATIN method and domain decomposition concepts; the method of Pierres et al [49] based on the LATIN method and augmented Lagrangian methods; the method of Ben Dhia and Jamond [7] which combines the extended FEM (XFEM) with the Arlequin method; the method of Galland et al [24] based on global model reduction. A recent version of the s-method aimed at multi-scale failure simulations, is the reduced order s-method (rs-method) of Fish et al [21,43].…”

Section: Introductionmentioning

confidence: 99%

A two-scale approach for the analysis of propagating three-dimensional fractures

2011

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This paper presents a generalized finite element method (GFEM) for crack growth simulations based on a two-scale decomposition of the solution-a smooth coarsescale component and a singular fine-scale component. The smooth component is approximated by discretizations defined on coarse finite element meshes. The fine-scale component is approximated by the solution of local problems defined in neighborhoods of cracks. Boundary conditions for the local problems are provided by the available solution at a crack growth step. The methodology enables accurate modeling of 3-D propagating cracks on meshes with elements that are orders of magnitude larger than those required by the FEM. The coarse-scale mesh remains unchanged during the simulation. This, combined with the hierarchical nature of GFEM shape functions, allows the recycling of the factorization of the global stiffness matrix during a crack growth simulation. Numerical examples demonstrating the approximating properties of the proposed enrichment functions and the computational performance of the methodology are presented.

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“…There are several other multiscale models available in literature, e.g., see Refs. [14][15][16][17][18], and the underlying idea of those methods is to impose constraints at nodes on mismatching interfaces to connect different scale meshes. Those methods however often require some modifications on the system matrix whenever the constraints are imposed [19].…”

Section: Introductionmentioning

confidence: 99%

3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks

Wang

Bui

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. analysts to gain a desirable accuracy with a few trials, which is suited for practices purpose.

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A two-scale extended finite element method for modelling 3D crack growth with interfacial contact

Cited by 38 publications

References 30 publications

A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method

A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method

A two-scale approach for the analysis of propagating three-dimensional fractures

3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks

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