Cohesive crack propagation analysis using a dipole BEM formulation with tangent operator

Almeida, Luís Philipe Ribeiro; Lima, Eduardo Toledo de; Barbirato, João Carlos Cordeiro

doi:10.1016/j.tafmec.2020.102765

Cited by 7 publications

(4 citation statements)

References 29 publications

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“…The dimensionless load and deflection values have been utilised for this purpose. The dimensionless load relates the reaction forces 𝑃𝑃 1 and 𝑃𝑃 2 at the supports to the prescribed displacement to geometrical and material parameters as follows:   (28) in which 𝑓𝑓 𝑇𝑇 is the tensile material strength and 𝑑𝑑 and 𝑡𝑡 are, respectively, the specimen's height and the thickness. Besides, the dimensionless displacement corresponds to the division between 6.10 4 times the applied displacement and the specimen's height.…”

Section: Four-point Bending Problem Multiple Cohesive Crack Growthmentioning

confidence: 99%

“…The BEM does not require domain mesh, which enables accurate assessment of internal mechanical fields and non-complex remeshing procedures during the crack growth. Several BEM formulations have been proposed in the literature for the solution of fracture problems, such as single-domain technique [26], multi-domain technique [27], dipoles approach [28] and cells with embedded discontinuities [29], for instance. Nevertheless, the robust BEM approach in fracture mechanics is the dual BEM (DBEM) formulation [24], [30].…”

Section: Introductionmentioning

confidence: 99%

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The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

Rocha

Leonel

2022

Rev. IBRACON Estrut. Mater.

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This study applies the Boundary Element Method (BEM) for the fracture failure modelling of three-dimensional concrete structures subjected to concentrated boundary conditions. The non-requirement of domain mesh by the BEM enables high accuracy in the domain fields assessment in addition to less complex remeshing procedures during crack propagation. However, concentrated boundary conditions often occur in fracture mechanics. The Lagrangian version of the BEM enforces such boundary conditions approximately by small length elements, which lead to numerical instabilities or even inaccurate problem representation. This study proposes a formulation for representing properly concentrated boundary conditions within the Lagrangian BEM framework. Nonlinear fracture mechanics describes the material failure processes herein. The classical cohesive crack approach governs the nonlinear energy dissipation processes, in which constant and tangent operators solve the resulting nonlinear system. Three applications demonstrate the accuracy of the proposed formulation, in which the BEM responses are compared against numerical and experimental results available in the literature.

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Section: Four-point Bending Problem Multiple Cohesive Crack Growthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

Rocha

Leonel

2022

Rev. IBRACON Estrut. Mater.

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“…The present study extends the dipole-based approach, 55,56 to the three dimensional context, which is the novelty herein. The original contribution involves the integral kernels associated to degeneration of the stress field along the FPZ surface and its mechanical influence into the internal and boundary mechanical fields.…”

Section: Introductionmentioning

confidence: 96%

“…The formulation described in reference 55 demonstrates excellent accuracy in the mechanical modelling of fracture processes in quasi‐brittle materials. Recently, Almeida et al 56 presented further developments in this formulation, in which comprehensive cohesive crack propagation analyses with tangent operator scheme have been introduced. In spite of its accuracy and effectivity, the dipole‐based BEM formulation has been limited to two‐dimensional domain, until the present.…”

Section: Introductionmentioning

confidence: 99%

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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Probabilistic dipole BEM model for cohesive crack propagation analysis

Almeida

Lima

Barbirato

2022

J Braz. Soc. Mech. Sci. Eng.

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Cohesive crack propagation analysis using a dipole BEM formulation with tangent operator

Cited by 7 publications

References 29 publications

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

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

Probabilistic dipole BEM model for cohesive crack propagation analysis

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