The boundary finite element method for predicting directions of cracks emerging from notches at bimaterial junctions

Müller, Axel H. E.; Wenck, J.; Goswami, Sanjib; Lindemann, J.; Hohe, Jörg; Becker, Wilfried

doi:10.1016/j.engfracmech.2004.04.004

Cited by 20 publications

(7 citation statements)

References 8 publications

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“…where Z is a Hamiltonian coefficient matrix (11) and the block-diagonal Schur decomposition [22] decouples Eqn. 10.…”

Section: Summary Of Sbfem Theorymentioning

confidence: 99%

“…SBFEM's analytic solution in radial direction, which enables the robust transition between power and power-logarithmic singularities [24] permitted the investigation of various multi-material scenarios without a priori knowledge of the order of singularity. Hence, multi-material plates under both static and dynamic loading [23] as well as the crack propagation direction at bi-material notches [11] have been studied. SBFEM was first extended to modelling crack propagation problems by Yang et al [35].…”

Section: Introductionmentioning

confidence: 99%

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A scaled boundary multiscale approach to crack propagation

Egger¹

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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In this work, we fuse the scaled boundary finite element method (SBFEM) on balanced hybrid quadtree-polygon (QT) meshes with the extended multiscale finite element method (EMsFEM) to accelerate crack propagation simulations. This scaled boundary multiscale approach to crack propagation employs SBFEM in a fully resolved region immediately surrounding the crack tip and coarse elements, i.e., EMsFEM unit cells, in the remaining domain. As the crack propagates across the domain, unit cells within the immediate crack path are resolved. Once the crack completely transitions a resolved unit cell it is replaced by two newly constructed, coarse unit cells. This approach limits computational effort to the crack tip region, primarily replacing the fine mesh on the domain by a coarse one, on which the governing equations are solved. Early results indicate that this method results in a reduction of required degrees of freedom (DOFs) by at least an order of magnitude for simple domains. Further techniques, unique to the SBFEM, are exploited to enrich the crack tip element and further reduce the amount of refinement necessary about the crack tip. The latter traditionally negatively affects the QT mesh due to the balancing operation. Via fusion of these two techniques, the amount of DOFs during simulations of crack propagation remains tractable.

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“…where Z is a Hamiltonian coefficient matrix (11) and the block-diagonal Schur decomposition [22] decouples Eqn. 10.…”

Section: Summary Of Sbfem Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A scaled boundary multiscale approach to crack propagation

Egger¹

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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“…Deeks and Wolf (2002). The two-dimensional application of the SBFEM in crack and notch problems can be found in the literature (Song and Wolf 1997, 1999, 2000Deeks 2002;Müller et al 2004;Chidgzey and Deeks 2005;Yang and Deeks 2007;Chidgzey et al 2008;Bird et al 2010). The application of SBFEM in three-dimensional structures is still rare, but some interesting studies can be found in ref.…”

Section: Introductionmentioning

confidence: 97%

Computation of 3-D stress singularities for multiple cracks and crack intersections by the scaled boundary finite element method

Goswami

Becker

2012

Int J Fract

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Among the various possible ways of dealing with notch and crack situations, the scaled boundary finite element method [SBFEM, (Wolf and Song in Finite element modelling of unbounded structures. Wiley, Chichester, 1996; Wolf in The scaled boundary finite element method. Wiley, Chichester, 2003)]has been adopted in this work. This method has been proved to be versatile, much less time consuming than the finite element method and generates highly accurate numerical predictions in cases of structures with notches and cracks. The SBFEM gives the advantage of boundary element method by reducing one dimension in modelling the structures but the mathematical formulations are more related to conventional displacement based finite element method. This method requires a certain scalability of the given structure with respect to a point called similarity center. Like in the case of the boundary element method, the structure needs to be discretized only at the surface where standard displacement based isoparametric finite element formulations are adequate. Unlike in the boundary element method, however, no fundamental solution is required by the scaled boundary finite element method. The similarity or scalability of the method requires separation of coordinates such that in the radial direction (i.e. scaling direction) it yields simple differential equations that can be solved analytically. So this approach can be considered as a semi-analytical method. Several two-dimensional examples have been analysed for crack and notch situations that are well known cases in fracture mechanics. A number of three-dimensional cases have been considered for different crack configurations that yield high order of singularity. The results, according to the authors' knowledge are up to now unpublished in the open literature. Parametric studies are conducted for structures with bi-material interfaces.

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“…Bi-materials are finding increasing applications in aerospace, automotive, marine and microelectronic structures [27,7,23,8,22,40]. Therefore, it becomes important to study the stress singularities and failure criteria at bi-material corners or notches [32] in order to ensure better design.…”

Section: Introductionmentioning

confidence: 99%

An experimental study on the crack initiation from notches connected to interfaces of bonded bi-materials

Krishnan

2013

Engineering Fracture Mechanics

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The boundary finite element method for predicting directions of cracks emerging from notches at bimaterial junctions

Cited by 20 publications

References 8 publications

A scaled boundary multiscale approach to crack propagation

A scaled boundary multiscale approach to crack propagation

Computation of 3-D stress singularities for multiple cracks and crack intersections by the scaled boundary finite element method

An experimental study on the crack initiation from notches connected to interfaces of bonded bi-materials

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