Three-dimensional crack growth simulation using BEM

Mi, Y.; Aliabadi, M.H.

doi:10.1016/0045-7949(94)90072-8

Cited by 152 publications

(52 citation statements)

References 13 publications

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“…Due to the dimension-reduction, the remeshing procedure is fairly simple as the crack is part of the boundary. Interesting applications of the BEM to fracture can be found, for example, in [240][241][242][243][244][245][246][247][248][249][250][251][252][253][254][255][256][257].…”

Section: Boundary Element Methodmentioning

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

160

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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: Boundary Element Methodmentioning

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

160

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“…The latter finds more use in three-dimensional applications [17]; in the present work the MPS criterion is applied as proposed by Erdogan and Sih [18]. Near the crack tip the maximum principal stress is taken as the tangential stress σ θθ , the singular part of which is given by…”

Section: The Dual Bem For Fatigue Crack Growthmentioning

confidence: 99%

Boundary element simulation of fatigue crack growth in multi-site damage

Price

Trevelyan

2014

Engineering Analysis with Boundary Elements

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(2014) 'Boundary element simulation of fatigue crack growth in multi-site damage.', Engineering analysis with boundary elements., 43 . pp. 67-75. Further information on publisher's website:http://dx.doi.org/10. 1016/j.enganabound.2014.03.002 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Engineering Analysis with Boundary Elements. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Engineering Analysis with Boundary Elements, 43, 2014, 10.1016/j.enganabound.2014.03.002. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThis paper presents an efficient and automatic scheme for modelling the growth of multiple cracks through a two-dimensional domain under fatigue loading based on linear elastic fracture mechanics. The dual boundary element method is applied to perform an analysis of the cracked domain and the J-integral technique is used to compute stress intensity factors. Incremental crack propagation directions are evaluated using the maximum principal stress criterion and a combined predictor-corrector algorithm implemented for propagation angle and increment length. Criteria are presented to control the mesh used on the slower growing cracks in the domain, improving computational efficiency and accuracy by the use of virtual crack tips to avoid the need for severe mesh grading. Results are presented for several geometries with multi-site damage, and sensitivity to incremental crack length is investigated. The scheme demonstrates considerable advantages over the finite element method for this application due to simplicity of meshing, and over other boundary element formulations for modelling domains with large ranges of crack growth rates.

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“…In the coupled method, the fast marching method maintains the location and motion of the crack front via signed distance functions, whereas the X-FEM is used to compute the local front velocity. In keeping with standard level set notation, we use in three dimensions are: finite element methods [12,13], boundary element-based techniques [14][15][16][17][18][19], and boundary integral equations [20,21]. Gao and Rice [22] and Lai et al [23] used perturbation analysis to study planar and non-planar cracks, whereas Lazarus and coworkers [24][25][26] conducted planar crack growth simulations.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method

Sukumar

Chopp

Béchet

et al. 2008

Numerical Meth Engineering

113

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SUMMARYA numerical technique for non-planar three-dimensional linear elastic crack growth simulations is proposed. This technique couples the extended finite element method and the fast marching method.In crack modeling using the extended finite element method, the framework of partition of unity is used to enrich the standard finite element approximation by a discontinuous function and the twodimensional asymptotic crack-tip displacement fields. The initial crack geometry is represented by two level set functions, and subsequently signed distance functions are used to maintain the location of the crack and to compute the enrichment functions that appear in the displacement approximation.Crack modeling is performed without the need to mesh the crack, and crack propagation is simulated * Correspondence to: N. Sukumar,

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Three-dimensional crack growth simulation using BEM

Cited by 152 publications

References 13 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

Boundary element simulation of fatigue crack growth in multi-site damage

Three‐dimensional non‐planar crack growth by a coupled extended finite element and fast marching method

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