Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons
- Authors: Chiong, Irene , Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 131, no. (2014), p. 210-231
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- Description: In this paper, the recently developed scaled boundary polygons formulation for the evaluation of stress intensity factors in functionally graded materials is extended to elasto-dynamics. In this approach, the domain is discretized using polygons with arbitrary number of sides. Within each polygon, the scaled boundary polygon shape functions are used to interpolate the displacement field. For uncracked polygons, these shape functions are linearly complete. In a cracked polygon, the shape functions analytically model the stress singularity at the crack tip. Therefore, accurate dynamic stress intensity factors can be computed directly from their definitions. Only a single polygon is necessary to accurately compute the stress intensity factors. To model the material heterogeneity in functionally graded materials, the material gradients are approximated locally in each polygon using polynomial functions. This leads to semi-analytical expressions for both the stiffness and the mass matrices, which can be integrated straightforwardly. The versatility of the developed formulation is demonstrated by modeling five numerical examples involving cracked functionally graded specimens subjected to dynamic loads. © 2014 Elsevier Ltd.
Finite fracture mechanics analysis using the scaled boundary finite element method
- Authors: Sun, Zhicheng , Ooi, Ean Tat , Song, Chongmin
- Date: 2015
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 134, no. (2015), p. 330-353
- Full Text: false
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- Description: The polygon-based scaled boundary finite element method is applied to two finite fracture mechanics based failure criteria to predict the crack initiation from stress concentrations, i.e. notches and holes. The stress and displacement fields are modelled by the scaled boundary finite element method through semi-analytical expressions that resemble asymptotic expansions around cracks and notches. Important fracture parameters, i.e. energy release rate and stress, are accurately and conveniently computed from the solutions of stresses and displacements via analytical integration. One distinguished advantage of applying the scaled boundary finite element method to finite fracture mechanics is that the required changes in the mesh are easily accommodated by shifting the crack tip within the cracked polygon without changing the global mesh structure. The developed framework is validated using four numerical examples. The crack initiation predictions obtained from the scaled boundary finite element method agree well with the reference finite element results.
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.
Modelling strong and weak discontinuities with the scaled boundary finite element method through enrichment
- Authors: Jiang, Shou-yan , Du, Chengbin , Ooi, Ean
- Date: 2019
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 222, no. (Dec 2019), p. 25
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- Description: In this paper, a technique to model strong and weak discontinuities with the scaled boundary finite element method through enrichment is proposed. The main advantage of the method is that the enriched elements, in the spirit of the extended finite element method (XFEM), do not need to physically conform to the geometry of features, e.g. internal interfaces and cracks, and remeshing is unnecessary as the interfaces evolve. All the advantages of the SBFEM and the XFEM are retained. The stress singularity at the crack tip can be captured accurately and the stress intensity factors (SIFs) can be directly computed based on the singular displacement or stress at the crack tip within the framework of the SBFEM. The numerical properties and performance for the proposed method are assessed using several numerical examples. In particular, problems with discontinuities, e.g. voids, inclusions, and cracks are analysed. The results show that the accuracy and convergence rate of the new approach for solving void or inclusion problems are identical to those of the XFEM, but requires less number of degrees-of-freedom than the XFEM. For crack problems, compared with the XFEM with topological enrichment, the developed method is superior.
A polygon scaled boundary finite element formulation for transient coupled thermoelastic fracture problems
- Authors: Ooi, Ean Tat , Iqbal, M. , Birk, C. , Natarajan, Sundararajan , Ooi, E. H. , Song, C.
- Date: 2020
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 240, no. (2020), p.
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- Description: The scaled boundary finite element method is developed for transient thermoelastic fracture analysis. To enable this, a set of novel shape functions are derived considering thermoelastic equilibrium. The salient features of the proposed framework are: (a) can be formulated on polygons with an arbitrary number of sides leading to flexible mesh generation and (b) facilitates an accurate and direct evaluation of the stress intensity factors from their definition without resorting to any post-processing techniques using relatively coarse meshes. Several numerical benchmark problems demonstrate the aforementioned features of the technique. © 2020 Elsevier Ltd