The scaled boundary finite element method for the analysis of 3D crack interaction

Hell, Sascha; Becker, Wilfried

doi:10.1016/j.jocs.2015.04.007

Cited by 25 publications

(14 citation statements)

References 11 publications

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“…First, the situation of a simple crack in an isotropic homogeneous material is considered as a benchmark example before we proceed to the more complex structural situation of two meeting cracks as it has been studied in [16].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…2b) studied in [16] is revisited and the convergence behavior of the first six eigenvalues resulting in stress singularities is investigated. The associated deformation modes are depicted and labeled in figure 7.…”

Section: Two Meeting Cracks In Homogeneous Isotropic Continuummentioning

confidence: 99%

“…In section 3, its advantages regarding accuracy and convergence are demonstrated for the generic examples of a simple crack [1,25] and two meeting cracks in a homogeneous isotropic cube [16]. Section 4 contains the major conclusions of our analyses.…”

Section: Introductionmentioning

confidence: 99%

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The Use of Enriched Base Functions in the Three-Dimensional Scaled Boundary Finite Element Method

Hell¹,

Becker²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The Scaled Boundary Finite Element Method (SBFEM) is a semi-analytical method which combines the advantages of the Boundary Element Method (BEM) and the Finite Element Method (FEM). Like in the BEM, only the boundary needs to be discretized. On the other hand, the SBFEM is based on the virtual work principle and does not need any fundamental solutions. If the scalability condition is fulfilled, a separation of variables representation can be employed leading to a quadratic eigenvalue problem and a linear equation system which can be solved by standard methods. The SBFEM has proven its high efficiency and accuracy in the presence of stress singularities, especially in 2D fracture mechanics when the singularity is entirely located within the considered domain.However, in 3D elasticity problems, there can also be singularities on the discretized boundary itself. Then, the SBFEM suffers from drawbacks also well known from the standard FEM, i.e. moderate accuracy and bad convergence. To overcome these deficiencies in such 3D cases, we propose the enrichment of the standard separation of variables representation with analytical fields which are known to exactly fulfill the local boundary conditions:The examples of a single plane crack and two perpendicularly meeting cracks in an isotropic continuum are considered. It is demonstrated that the method's original excellent accuracy and convergence are regained, at a minimum cost of additional degrees of freedom (DOF). The normalized errors in the solution of the quadratic eigenvalue problem already become negligibly small for very coarse boundary meshes. The obtained convergence orders are often optimal and sometimes even superconvergence is observed.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Two Meeting Cracks In Homogeneous Isotropic Continuummentioning

confidence: 99%

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The Use of Enriched Base Functions in the Three-Dimensional Scaled Boundary Finite Element Method

Hell¹,

Becker²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…The method has been improved to solve non-homogeneous anisotropic heat conduction problems [69]. 3D crack interaction may be analyzed now with SBFEM [70]. Modeling wave propagation in semi-infinite domain is possible to be modeled efficiently with SBFEM, as can be found in [71] in which complex inclined soil field are explained how to be modeled in order to account for SSI.…”

Section: The Scaled-boundary Finite Element Methodsmentioning

confidence: 99%

2-D soil-structure interaction in time domain by the SBFEM and two non-linear soil models

Rahnema

Mohasseb

JavidSharifi

2016

Soil Dynamics and Earthquake Engineering

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“…In order to use the boundary element method, one only needs to fit the boundary of the system without calculation of parameters inside the solid body analysed, so the dimension of the problem can decrease and the size of the algebraic equations can be considerably smaller than the finite element equation [1,2]. In the area of fracture mechanics and mechanical engineering, some researchers have utilised the boundary element method [3,4], the Voronoi tesselation method [5] or the finite element method [6,7]. These methods are very suitable for use in determining the behaviour of a solid body which contains several cracks and holes.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Crack Initiation and Propagation in a Piezoelectric Ceramic Using the Boundary Element Method

Stachowicz

Biglar

Gromada

et al. 2017

Acta Metall Slovaca

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The subject of this paper is the analysis of crack initiation and propagation in barium titanate ceramic using the boundary element method. In micro-mechanical analyses, it is very important to have information on the real microstructure of a material. A barium titanate pellet was prepared using a solid-state technique. The boundary element method is used so that it can be combined with three different grain boundary formulations for the investigation of micromechanics as well as crack initiation and propagation in a piezoelectric actuator. In order to develop a numerical programming algorithm, suitable models of polycrystalline aggregate and representative volume elements have been prepared for boundary element analysis.Keywords: barium titanate, boundary element method, ceramics, microstructure IntroductionA The boundary element method (BEM) is one of the favourite optimised numerical computational methods used by scientists in many areas of engineering and science including fracture mechanics, fluid mechanics, and geology. In order to use the boundary element method, one only needs to fit the boundary of the system without calculation of parameters inside the solid body analysed, so the dimension of the problem can decrease and the size of the algebraic equations can be considerably smaller than the finite element equation [1,2]. In the area of fracture mechanics and mechanical engineering, some researchers have utilised the boundary element method [3,4], the Voronoi tesselation method [5] or the finite element method [6,7]. These methods are very suitable for use in determining the behaviour of a solid body which contains several cracks and holes. It is worth mentioning that both finite and infinite bodies can be studied via the BEM. In order to use this method, one must pay attention to the fact that the traction fundamental solution and displacement fundamental solution for isotropic bodies are different to those for anisotropic bodies. This is the most important fact that researchers have to consider before using the BEM [8,9] or discrete element method [10] for investigations. The application of the boundary element method in micromechanics and multiscale modelling has been studied by a number of researchers [11][12][13]. In some of these studies, researchers only modelled materials at micro scale and with the cohesive law, averaging theory or nonlocal theories were not used. Several researchers have utilised some basic concepts

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The scaled boundary finite element method for the analysis of 3D crack interaction

Cited by 25 publications

References 11 publications

The Use of Enriched Base Functions in the Three-Dimensional Scaled Boundary Finite Element Method

The Use of Enriched Base Functions in the Three-Dimensional Scaled Boundary Finite Element Method

2-D soil-structure interaction in time domain by the SBFEM and two non-linear soil models

Analysis of Crack Initiation and Propagation in a Piezoelectric Ceramic Using the Boundary Element Method

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