A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics
- Authors: Song, Chongmin , Ooi, Ean Tat , Natarajan, Sundararajan
- Date: 2018
- Type: Text , Journal article , Review
- Relation: Engineering Fracture Mechanics Vol. 187, no. (2018), p. 45-73
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- Description: The development and the application of the scaled boundary finite element method for fracture analysis is reviewed. In this method, polygonal elements (referred to as subdomains) of arbitrary number of edges are constructed, with the only limitation that the whole boundary is directly visible from the scaling centre. The element solution is semi-analytical. When applied to two-dimensional linear fracture mechanics, any kinds of stress singularities are represented analytically without local refinement, special elements and enrichment functions. The flexibility of polygons to represent arbitrary geometric shapes leads to simple yet efficient remeshing algorithms to model crack propagation. Coupling procedures with the extended finite element method, meshless method and boundary element method to handle changes in the crack morphology have been established. These developments result in an efficient framework for fracture modelling. Examples of applications are provided to demonstrate their feasibility. © 2017 Elsevier Ltd
Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling
- Authors: Ooi, Ean Tat , Man, Hou , Natarajan, Sundararajan , Song, Chongmin
- Date: 2015
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 144, no. (2015), p. 101-117
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- Description: A crack propagation modelling technique combining the scaled boundary finite element method and quadtree meshes is developed. This technique automatically satisfies the compatibility requirement between adjacent quadtree cells irrespective of the presence of hanging nodes. The quadtree structure facilitates efficient data storage and rapid computations. Only a single cell is required to accurately model the stress field near crack tips. Crack growth is modelled by splitting the cells in the mesh into two. The resulting polygons are directly modelled by the scaled boundary formulation with minimal changes to the mesh. Four numerical examples demonstrate the salient features of the technique. © 2015.
Automatic modelling of cohesive crack propagation in concrete using polygon scaled boundary finite elements
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis , Yang, Zhenjun
- Date: 2012
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 93, no. (2012), p. 13-33
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- Description: An automatic cohesive crack propagation modelling methodology for quasi-brittle materials using polygon elements is presented. Each polygon is treated as a subdomain that is modelled by the scaled boundary finite element method (SBFEM). Generalised stress intensity factors (SIFs) based on matrix power function solutions of singular stress fields obtained from the SBFEM following standard finite element stress recovery procedures is used to evaluate the crack propagation criterion and determine the crack propagation direction. Interface elements model the fracture process zones and are automatically inserted into the polygon mesh as the crack propagates. A shadow domain procedure couples the polygons and interface elements. It computes the load-displacement response and crack propagation criterion, taking into account the cohesive tractions on the crack edges that are modelled as side-face tractions in the SBFEM. Cracks are propagated using a simple, yet flexible local remeshing procedure that can remesh any arbitrary polygon. Only minimal changes are made to the global mesh structure each time the remeshing algorithm is called. Five cohesive crack propagation benchmarks are modelled to validate the developed method and demonstrate its salient features. © 2012 Elsevier Ltd.
Efficient prediction of deterministic size effects using the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Yang, Zhenjun
- Date: 2010
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 77, no. 6 (2010), p. 985-1000
- Full Text: false
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- Description: This paper develops an efficient numerical approach to predict deterministic size effects in structures made of quasi-brittle materials using the scaled boundary finite element method (SBFEM). Depending on the structure's size, two different SBFEM-based crack propagation modelling methodologies are used for fracture analyses. When the length of the fracture process zone (FPZ) in a structure is of the order of its characteristic dimension, nonlinear fracture analyses are carried out using the finite element-SBFEM coupled method. In large-sized structures, a linear elastic fracture mechanics (LEFM)-based SBFEM is used to reduce computing time due to small crack propagation length required to represent the FPZ in an equivalent nonlinear analysis. Remeshing is used in both methods to model crack propagation with crack paths unknown a priori. The resulting peak loads are used to establish the size effect laws. Three concrete structures were modelled to validate the approach. The predicted size effect is in good agreement with experimental data. The developed approach was found more efficient than the finite element method, at least in modelling LEFM problems and is thus an attractive tool for predicting size effect. © 2010 Elsevier Ltd.