A finite element method for crack growth without remeshing

Moës, Nicolas; Dolbow, John E.; Belytschko, Ted

doi:10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j

Cited by 5,272 publications

(1,854 citation statements)

References 13 publications

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“…To model the cohesive cracks in XFEM [Moës et al 1999;Strouboulis et al 2001;Babuška et al 2003;Karihaloo and Xiao 2003], a standard local FE displacement approximation around the crack is enriched with discontinuous Heaviside functions along the crack faces behind the crack tip including the open traction-free part, and the crack tip asymptotic displacement fields at nodes surrounding the cohesive crack tip using the PU. The approximation of displacements for an element can be expressed in the form…”

Section: Implementation In Xfemmentioning

confidence: 99%

“…The knowledge of the asymptotic crack tip displacement fields is especially useful in the recently developed extended finite element methodology (XFEM) (see [Moës et al 1999;Strouboulis et al 2001;Babuška et al 2003;Karihaloo and Xiao 2003], for example). XFEM enriches the standard local FE approximations with known information about the problem, with the use of the partition of unity (PU).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

Karihaloo

Xiao

2011

J. Mech. Mater. Struct.

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The extended finite element (XFEM) enriches the standard local FE approximations with known information about the problem, with the use of the partition of unity. This allows the use of meshes that do not conform to a discontinuity and avoids adaptive re-meshing as the discontinuity grows as required with the conventional FEM. When the crack tip asymptotic field is available and used as the enrichment function, XFEM is more accurate than FEM allowing the use of a much coarser mesh around the crack tip. Such asymptotic fields have been known for a long time for traction-free cracks (the Williams expansions) but have only recently been derived for cohesive cracks (Karihaloo-Xiao expansions). In this paper an overview of latter expansions is given for a range of cohesive laws and their usefulness in the simulation of cohesive crack propagation is demonstrated on two examples of concrete and fibre-reinforced concrete flexural members.

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Section: Implementation In Xfemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

Karihaloo

Xiao

2011

J. Mech. Mater. Struct.

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“…The PoU theory allows for the addition of a priori solution of a boundary-value problem into the approximation spaces through numerical enrichment schemes. Thus, an FE mesh does not have to conform to structural boundaries or crack surfaces [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Augmented finite-element method for arbitrary cracking and crack interaction in solids under thermo-mechanical loadings

Jung¹,

C.²,

Yang³

2016

Phil. Trans. R. Soc. A.

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In this paper, a thermal-mechanical augmented finiteelement method (TM-AFEM) has been proposed, implemented and validated for steady-state and transient, coupled thermal-mechanical analyses of complex materials with explicit consideration of arbitrary evolving cracks. The method permits the derivation of explicit, fully condensed thermalmechanical equilibrium equations which are of mathematical exactness in the piece-wise linear sense. The method has been implemented with a 4-node quadrilateral two-dimensional (2D) element and a 4-node tetrahedron three-dimensional (3D) element. It has been demonstrated, through several numerical examples that the new TM-AFEM can provide significantly improved numerical accuracy and efficiency when dealing with crack propagation problems in 2D and 3D solids under coupled thermalmechanical loading conditions.

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“…In order to alleviate the mesh-dependency inherent to the intrinsic cohesive approach, the eXtended (or Generalized) Finite Element Method (XFEM) [35] has been used in combination with CZM [36,37] for predicting fracture mechanisms. XFEM offers the possibility to represent the entire crack geometry independently of the mesh, so that refined meshes are not necessary to model crack growth.…”

Section: Introductionmentioning

confidence: 99%

An XFEM/CZM implementation for massively parallel simulations of composites fracture

Vigueras

Sket

Samaniego

et al. 2015

Composite Structures

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Because of their widely spread use in many industries, composites are the subject of many research campaigns. More particularly, the development of both accurate and flexible numerical models able to capture their intrinsically multiscale modes of failure is still a challenge. The standard finite element method typically requires intensive remeshing to adequately capture the geometry of the cracks and high accuracy is thus often sacrificed in favor of scalability, and vice versa. In an effort to preserve both properties, we present here an extended finite element method (XFEM) for large scale composite fracture simulations. In this formulation, the standard FEM formulation is partially enriched by use of shifted Heaviside functions with special attention paid to the scalability of the scheme. This enrichment technique offers several benefits, since the interpolation property of the standard shape function still holds at the nodes. Those benefits include (i) no extra boundary condition for the enrichment degree of freedom, and (ii) no need for transition/blending regions; both of which contribute to maintain the scalability of the code.Two different cohesive zone models (CZM) are then adopted to capture the physics of the crack propagation mechanisms. At the intralaminar level, an extrinsic CZM embedded in the XFEM formulation is used. At the interlaminar level, an intrinsic CZM is adopted for predicting the failure. The overall framework is implemented in ALYA, a mechanics code specifically developed for large scale, massively parallel simulations of coupled multi-physics problems. The implementation of both intrinsic and extrinsic CZM models within the code is such that it conserves the extremely efficient scalability of ALYA while providing accurate physical simulations of computationally expensive phenomena. The strong scalability provided by the proposed implementation is demonstrated. The model is ultimately validated against a full experimental campaign of loading tests and X-ray tomography analyses for a chosen very large scale.

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A finite element method for crack growth without remeshing

Cited by 5,272 publications

References 13 publications

Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

Augmented finite-element method for arbitrary cracking and crack interaction in solids under thermo-mechanical loadings

An XFEM/CZM implementation for massively parallel simulations of composites fracture

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