Cohesive crack growth modelling based on an alternative nonlinear BEM formulation

Oliveira, Hugo Luiz; Leonel, Edson Denner

doi:10.1016/j.engfracmech.2013.09.003

Cited by 40 publications

(17 citation statements)

References 24 publications

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“…According to the curves presented in Figures 19 and 20, good agreement is observed among the numerical responses achieved by sub-region BEM approaches implemented and by references [6,7]. The responses achieved by the implemented sub-region BEM approaches are more rigid in comparison with experimental results.…”

Section: Mixed Mode Crack Growth In a Bended Beammentioning

confidence: 52%

“…This structure was analysed experimentally by Saleh et al, [14] and numerically by Oliveira et al, [6,7]. The geometry, boundary conditions and material Cohesive interface 2m 2m properties of the problem are presented in Figure 11.…”

Section: Three Point Bended Beammentioning

confidence: 99%

“…This structure was experimentally analysed by [15] and numerically studied by several authors, among them [6,7]. The structural geometry, boundary conditions and material properties are presented in Figure 16.…”

Section: Mixed Mode Crack Growth In a Bended Beammentioning

confidence: 99%

“…To model the crack growth process in quasi-brittle materials, cohesive crack approach, by the fictitious crack model, is an interesting alternative. This approach was initially applied by [3][4][5] and extensively used in recent numerical applications [6][7][8][9]. The crack propagation modelling of quasi-brittle materials, based on cohesive approach, requires the solution of a nonlinear problem, generally relating the crack opening displacements (COD) to tractions on the crack surfaces.…”

Section: Introductionmentioning

confidence: 99%

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Cohesive Discontinuities Growth Analysis using a Nonlinear Boundary Element Formulation

Ed¹,

Gfc²

2014

J Appl Computat Math

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Section: Mixed Mode Crack Growth In a Bended Beammentioning

confidence: 52%

Section: Three Point Bended Beammentioning

confidence: 99%

Section: Mixed Mode Crack Growth In a Bended Beammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cohesive Discontinuities Growth Analysis using a Nonlinear Boundary Element Formulation

Ed¹,

Gfc²

2014

J Appl Computat Math

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“…If we consider the boundary element method as a means for solving this problem, nonlinear behaviour may occur [18]. Thus, it is necessary for the macro scale to be simulated via a nonlinear boundary element formulation in order to exploit the local nonlinear behaviour of the material.…”

Section: Application Of Bem At Macro Scalementioning

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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Dipole‐based BEM formulation for three‐dimensional cohesive crack propagation modelling

Ribeiro Almeida,

Leonel

2024

Numerical Meth Engineering

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This study presents an alternative boundary element method (BEM) formulation for the cohesive crack propagation modelling in three‐dimensional structures. The proposed formulation utilises an initial stress field for representing the mechanical behaviour along the fracture process zone, which leads to a set of self‐equilibrated forces named as dipole. Cohesive laws govern the material nonlinear behaviour along the fracture process zone. The proposed dipole‐based formulation demonstrates some advantages in comparison to classical BEM approaches in this field. Among them, it is worth citing the requirement of solely three integral equations per collocation point positioned at the fracture process zone. The effectiveness of the dipole‐based formulation has been demonstrated by four applications. The results have been compared to numerical, experimental and analytical solutions available in the literature, in which excellent performance has been observed.

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Cohesive crack growth modelling based on an alternative nonlinear BEM formulation

Cited by 40 publications

References 24 publications

Cohesive Discontinuities Growth Analysis using a Nonlinear Boundary Element Formulation

Cohesive Discontinuities Growth Analysis using a Nonlinear Boundary Element Formulation

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

Dipole‐based BEM formulation for three‐dimensional cohesive crack propagation modelling

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