Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

Jäger, Philippe; Steinmann, Paul; Kuhl, Ellen

doi:10.1007/s00466-009-0417-0

Cited by 18 publications

(11 citation statements)

References 67 publications

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“…Equation (45) can be rephrased as an anisotropic heat conduction problem [101,276,277]. The drawback of this method is that the heat conduction problem has to be solved at every time step making global methods computationally expensive.…”

Section: Global Methodsmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

162

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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Section: Global Methodsmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

162

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“…The idea is remarkably simple yet retains all the advantages associated with the level-set methods and is arguably more suited to being integrated in an existing general purpose finite element framework. Since the original paper by Oliver et al [24], the approach has been extensively used in both the E-FEM and X-FEM frameworks in several studies (see [25,26,27,28,29,30,31,32]). In 2D, a comparison between the global and explicit crack tracking approaches is presented in Dumstorff and Meschke [33,34].…”

Section: Introductionmentioning

confidence: 99%

“…Jäger et al [30,31,32] in a series of articles present a thorough analysis of the global crack tracking approach when used in conjunction with the phantom node method to model crack propagation in 3D. They compare and contrast the method's performance with the alternatives available and highlight the method's promise to model arbitrary crack propagation problems in 3D.…”

Section: Introductionmentioning

confidence: 99%

A local crack-tracking strategy to model three-dimensional crack propagation with embedded methods

Annavarapu

Settgast

Vitali

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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We develop a local, implicit crack tracking approach to propagate embedded failure surfaces in three-dimensions. We build on the global crack-tracking strategy of Oliver et al. (Int. J. Numer. Anal. Meth. Geomech., 2004; 28: 609-632) that tracks all potential failure surfaces in a problem at once by solving a Laplace equation with anisotropic conductivity. We discuss important modifications to this algorithm with a particular emphasis on the effect of the Dirichlet boundary conditions for the Laplace equation on the resultant crack path. Algorithmic and implementational details of the proposed method are provided. Finally, several three-dimensional benchmark problems are studied and results are compared with available literature. The results indicate that the proposed method addresses pathological cases, exhibits better behavior in the presence of closely interacting fractures, and provides a viable strategy to robustly evolve embedded failure surfaces in 3D.

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“…The case has been studied, e.g. by Dias-Da-Costa et al (2010), Gasser and Holzapfel (2006) and Jäger et al (2009) with very similar material parameters. Obtained crack propagation path is shown in Figure 11.…”

Section: Simulation Of Nooru-mohamed Testmentioning

confidence: 98%

A local remeshing procedure to simulate crack propagation in quasi‐brittle materials

Kuutti

Kolari

2012

Engineering Computations

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Purpose -The purpose of this paper is to present a new simplified local remeshing procedure for the study of discrete crack propagation in finite element (FE) mesh. The proposed technique accounts for the generation and propagation of crack-like failure within an FE-model. Beside crack propagation, the technique enables the analysis of fragmentation of initially intact continuum. The capability of modelling fragmentation is essential in various structure-structure interaction analyses such as projectile impact analysis and ice-structure interaction analysis. Design/methodology/approach -The procedure combines continuum damage mechanics (CDM), fictitious crack approach and a new local remeshing procedure. In the approach a fictitious crack is replaced by a discrete crack by applying delete-and-fill local remeshing. The proposed method is independent of mesh topology unlike the traditional discrete crack approach. The procedure is implemented for 3-D solid elements in commercial finite element software Abaqus/Explicit using Python scripting. The procedure is completely automated, such that crack initiation and propagation analyses do not require user intervention. A relatively simple constitutive model was implemented strictly for demonstrative purposes. Findings -Well known examples were simulated to verify the applicability of the method. The simulations revealed the capabilities of the method and reasonable correspondence with reference results was obtained. Material fragmentation was successfully simulated in ice-structure interaction analysis. Originality/value -The procedure for modelling discrete crack propagation and fragmentation of initially intact quasi-brittle materials based on local remeshing has not been presented previously. The procedure is well suited for simulation of fragmentation and is implemented in a commercial FE-software.

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Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

Cited by 18 publications

References 67 publications

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

A local crack-tracking strategy to model three-dimensional crack propagation with embedded methods

A local remeshing procedure to simulate crack propagation in quasi‐brittle materials

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