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
- Full Text: false
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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.
Crack propagation modelling in functionally graded materials using scaled boundary polygons
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Tin-Loi, Francis
- Date: 2015
- Type: Text , Journal article
- Relation: International Journal of Fracture Vol. Online first, no. 192 (2015), p. 87-105
- Full Text: false
- Reviewed:
- Description: A recently developed scaled boundary finite element formulation that can model the response of functionally graded materials is further developed to model crack propagation in two-dimensions. This formulation can accurately model the stress singularity at the crack tip in heterogeneous materials. The asymptotic behaviour at the crack tip is analytically represented in the scaled boundary shape functions of a cracked polygon. This enables accurate stress intensity factors to be computed directly from their definitions. Neither local mesh refinement nor asymptotic enrichment functions are required. This novel formulation can be implemented on polygons with an arbitrary number of sides. When modelling crack propagation, the remeshing process is more flexible and leads to only minimal changes to the global mesh structure. Six numerical examples involving crack propagation in functionally graded materials are modelled to demonstrate the salient features of the developed method.
Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon-quadtree meshes
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Ooi, Ean Hin
- Date: 2017
- Type: Text , Journal article
- Relation: International Journal of Fracture Vol. 203, no. 1-2 (2017), p. 135-157
- Full Text: false
- Reviewed:
- Description: This manuscript presents an extension of the recently-developed hybrid polygon-quadtree-based scaled boundary finite element method to model crack propagation in concrete. This hybrid approach combines the use of quadtree cells with arbitrary sided polygons for domain discretization. The scaled boundary finite element formulation does not distinguish between quadtree cells and arbitrary sided polygons in the mesh. A single formulation is applicable to all types of cells and polygons in the mesh. This eliminates the need to develop transitional elements to bridge the cells belonging to different levels in the quadtree hierarchy. Further to this, the use of arbitrary sided polygons facilitate the accurate discretization of curved boundaries that may result during crack propagation. The fracture process zone that is characteristic in concrete fracture is modelled using zero-thickness interface elements that are coupled to the scaled boundary finite element method using a shadow domain procedure. The scaled boundary finite element method can accurately model the asymptotic stress field in the vicinity of the crack tip with cohesive tractions. This leads to the accurate computation of the stress intensity factors, which is used to determine the condition for crack propagation and the resulting direction. Crack growth can be efficiently resolved using an efficient remeshing algorithm that employs a combination of quadtree decomposition functions and simple Booleans operations. The flexibility of the scaled boundary finite element method to be formulated on arbitrary sided polygons also result in a flexible remeshing algorithm for modelling crack propagation. The developed method is validated using three laboratory experiments of notched concrete beams subjected to different loading conditions.
Modelling dynamic crack propagation using the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Yang, Zhenjun
- Date: 2011
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 88, no. 4 (2011), p. 329-349
- Full Text: false
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- Description: This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi-analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack-tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode-I and mix-mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. © 2011 John Wiley & Sons, Ltd.
A hybrid finite element-scaled boundary finite element method for reinforced concrete modelling
- Authors: Ooi, Ean Tat , Yang, Zhenjun
- Date: 2010
- Type: Text , Conference paper
- Relation: 10th International Conference on Computational Structures Technology, CST 2010; Valencia; Spain; 14th-17th September, 2010 published in Civil-Comp Proceedings Vol. 93
- Full Text: false
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- Description: This paper develops a reinforced concrete model that is based on the novel hybrid finite element-scaled boundary finite element method for fully automatic multiple cohesive crack propagation in reinforced concrete beams. The hybrid method can efficiently extract accurate stress intensity factors from semi-analytical solutions of stresses or displacements and is also flexible in remeshing multiple cracks. The RC model lumps adjacent reinforcements into a layer of four-noded quadrilateral elements that is connected to the concrete bulk with cohesive interface elements. These elements model the concrete-steel interaction and consider both bond-slip and splitting tensile crack mechanisms. A reinforced concrete beam is modelled. The numerical results show good agreement with both experimental and numerical results available in literature. © Civil-Comp Press, 2010.
- Description: Civil-Comp Proceedings
Dynamic crack propagation simulation with scaled boundary polygon elements and automatic remeshing technique
- Authors: Ooi, Ean Tat , Shi, Mingguang , Song, Chongmin , Tin-Loi, Francis , Yang, Zhenjun
- Date: 2013
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 106, no. (2013), p. 1-21
- Full Text: false
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- Description: An efficient methodology for automatic dynamic crack propagation simulations using polygon elements is developed in this study. The polygon mesh is automatically generated from a Delaunay triangulated mesh. The formulation of an arbitrary n-sided polygon element is based on the scaled boundary finite element method (SBFEM). All kind of singular stress fields can be described by the matrix power function solution of a cracked polygon. Generalised dynamic stress intensity factors are evaluated using standard finite element stress recovery procedures. This technique does not require local mesh refinement around the crack tip, special purpose elements or nodal enrichment functions. An automatic local remeshing algorithm that can be applied to any polygon mesh is developed in this study to accommodate crack propagation. Each remeshing operation involves only a small patch of polygons around the crack tip, resulting in only minimal change to the global mesh structure. The increase of the number of degrees-of-freedom caused by crack propagation is moderate. The method is validated using four dynamic crack propagation benchmarks. The predicted dynamic fracture parameters show good agreement with experiment observations and numerical simulations reported in the literature. © 2013 Elsevier Ltd.
Polygon scaled boundary finite elements for crack propagation modelling
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis , Yang, Zhenjun
- Date: 2012
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 91, no. 3 (2012), p. 319-342
- Full Text: false
- Reviewed:
- Description: An automatic crack propagation modelling technique using polygon elements is presented. A simple algorithm to generate a polygon mesh from a Delaunay triangulated mesh is implemented. The polygon element formulation is constructed from the scaled boundary finite element method (SBFEM), treating each polygon as a SBFEM subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks. Stress intensity factors are computed directly from their definitions without any nodal enrichment functions. An automatic remeshing algorithm capable of handling any n-sided polygon is developed to accommodate crack propagation. The algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths. The efficiency of the polygon SBFEM in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack. Four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features. The predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature. © 2012 John Wiley & Sons, 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
- Full Text:
- Reviewed:
- 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.
Crack propagation modelling in functionally graded materials using scaled boundary polygons
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Tin-Loi, Francis
- Date: 2015
- Type: Text , Journal article
- Relation: International Journal of Fracture Vol. 192, no. 1 (2015), p. 87-105
- Full Text: false
- Reviewed:
- Description: A recently developed scaled boundary finite element formulation that can model the response of functionally graded materials is further developed to model crack propagation in two-dimensions. This formulation can accurately model the stress singularity at the crack tip in heterogeneous materials. The asymptotic behaviour at the crack tip is analytically represented in the scaled boundary shape functions of a cracked polygon. This enables accurate stress intensity factors to be computed directly from their definitions. Neither local mesh refinement nor asymptotic enrichment functions are required. This novel formulation can be implemented on polygons with an arbitrary number of sides. When modelling crack propagation, the remeshing process is more flexible and leads to only minimal changes to the global mesh structure. Six numerical examples involving crack propagation in functionally graded materials are modelled to demonstrate the salient features of the developed method. © 2015, Springer Science+Business Media Dordrecht.
A quadtree-based scaled boundary finite element method for crack propagation modelling
- Authors: Ooi, Ean Tat , Man, Hou , Natarajan, Sundararajan , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Conference paper
- Relation: 23rd Australasian Conference on the Mechanics of Structures and Materials, Byron Bay, NSW, 9-12 December, Southern Cross University, Lismore, NSW, p. 813-818
- Full Text:
- Reviewed:
- Description: The quadtree is a hierarchical-type data structure where each parent is recursively divided into four children. This structure makes it particularly efficient for adaptive mesh refinement in regions with localised gradients. Compared with unstructured triangles, mesh generation is more efficient using quadtree decompositions. The finite number of patterns in the quadtree decomposition makes it efficient for data storage and retrieval. Motivated by these advantages, a crack propagation modelling approach using a quadtree-based scaled boundary finite element method (SBFEM) is developed. Starting from the formulation of an arbitrary n-sided polygon element, each quadrant in the quadtree mesh is treated as a polygon within the framework of the SBFEM. Special techniques to treat the hanging nodes are not necessary. Moreover, the SBFEM enables accurate calculation of the stress intensity factors directly from its solutions without local mesh refinement or asymptotic enrichment functions. When a crack propagates, it is only necessary to split each quadrant cut by the crack into two. These quadrants are polygons that can be directly modelled by the SBFEM. Changes to the mesh are minimal. The efficiency of this approach is demonstrated using numerical benchmarks.
Dynamic cohesive crack propagation modelling using the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Yang, Zhenjun , Guo, Zaoyang
- Date: 2012
- Type: Text , Journal article
- Relation: Fatigue and Fracture of Engineering Materials and Structures Vol. 35, no. 8 (2012), p. 786-800
- Full Text: false
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- Description: This study develops a scaled boundary finite element method (SBFEM)-based approach for modelling fast cohesive crack propagation in quasi-brittle materials subjected to transient dynamic loadings. In this approach, the elastic bulk material is modelled by SBFEM subdomains and the cracks by nonlinear cohesive interface finite elements that are automatically inserted by a remeshing procedure. The global equation system is solved using an implicit time integration algorithm. Because all the solutions (displacements, stresses, velocities, accelerations) are semi-analytical in an SBFEM subdomain, this approach offers a few advantages over other methods, such as accurate calculation of dynamic stress intensity factors and T-stress without using fine crack-tip meshes, simpler remeshing, more accurate and efficient mesh mapping, and the need of much fewer degrees of freedom for the same accuracy. The approach is validated by modelling two concrete beams under impact, subjected to mode-I and mixed-mode fracture, respectively. © 2012 Blackwell Publishing Ltd.
A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials
- Authors: Chen, Xiaojun , Luo, Tao , Ooi, Ean Tat , Ooi, Ean Hin , Song, Chongmin
- Date: 2018
- Type: Text , Journal article
- Relation: Theoretical and Applied Fracture Mechanics Vol. 94, no. (2018), p. 120-133
- Full Text: false
- Reviewed:
- Description: This paper presents a method to improve the computational efficiency of the scaled boundary finite element formulation for functionally graded materials. Both isotropic and orthotropic functionally graded materials are considered. This is achieved using a combination of quadtree and polygon meshes. This hybrid meshing approach is particularly suitable to be used with the SBFEM for functionally graded materials because of the significant amount of calculations required to compute the stiffness matrices of the polygons/cells in the mesh. When a quadtree structure is adopted, most of the variables required for the numerical simulation can be pre-computed and stored in the memory, retrieved and scaled as required during the computations, leading to an efficient method for crack propagation modeling. The scaled boundary finite element formulation enables accurate computation of the stress intensity factors directly from the stress solutions without any special post-processing techniques or local mesh refinement in the vicinity of the crack tip. Numerical benchmarks demonstrate the efficiency of the proposed method as opposed to using a purely polygon-mesh based approach. © 2018 Elsevier Ltd
A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete
- Authors: Guo, H. , Ooi, Ean Tat , Saputra, Albert , Yang, Zhenjun , Natarajan, Sundararajan , Ooi, Ean Hin , Song, Chongmin
- Date: 2019
- Type: Text , Journal article , acceptedVersion
- Relation: Engineering Fracture Mechanics Vol. 211, no. (2019), p. 420-441
- Full Text:
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- Description: A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility.
Fracture analysis of cracked magneto-electro-elastic functionally graded materials using scaled boundary finite element method
- Authors: Nguyen, Duc , Javidan, Fatemeh , Attar, Mohammadmahdi , Natarajan, Sundararajan , Yang, Zhenjun , Ooi, Ean Hin , Song, Chongmin , Ooi, Ean Tat
- Date: 2022
- Type: Text , Journal article
- Relation: Theoretical and Applied Fracture Mechanics Vol. 118, no. (2022), p.
- Full Text: false
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- Description: This paper develops the scaled boundary finite element method to analyse fracture of functionally graded magneto-electro-elastic materials. Polygon meshes are employed to discretize the domain. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required to calculate the intensity factors. When the material gradients of the coefficients in the constitutive matrix are expressed as a series of power functions of the scaled boundary coordinates, the stiffness matrices can be integrated analytically. The formulation enables the generalized intensity factors of stress, electric displacement and magnetic induction fields along the radial direction to be represented analytically. This permits the calculation of the generalized intensity factors directly from the scaled boundary finite element solution of the singular stress, electric displacement and magnetic induction fields by following the standard stress recovery procedures in the finite element method. Several numerical benchmarks are presented to validate the proposed technique with the results reported in the literature. © 2022 Elsevier Ltd
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.
- Full Text: false
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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
Transient thermoelastic fracture analysis of functionally graded materials using the scaled boundary finite element method
- Authors: Iqbal, M. , Birk, Carolin , Ooi, Ean Tat , Natarajan, Sundararajan , Gravenkamp, Hauke
- Date: 2023
- Type: Text , Journal article
- Relation: Theoretical and Applied Fracture Mechanics Vol. 127, no. (2023), p.
- Full Text: false
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- Description: To model fracture in functionally graded materials (FGMs), the scaled boundary finite element method (SBFEM) is extended to examine the effects of fully coupled transient thermoelasticity. Previously developed SBFEM supplementary shape functions are utilized to model thermal stresses. The spatial variation of thermal and mechanical properties of FGMs are approximated by polynomial functions facilitating the semi-analytical evaluation of coefficient matrices. The dynamic stress intensity factors (SIFs) are also evaluated semi-analytically from their definitions without the need for additional post-processing. Scaled boundary polygon elements are employed to facilitate the meshing of complex crack geometries. Both isotropic and orthotropic materials with different material gradation functions are considered. To study the transient effects of thermoelasticity on fracture parameters, several numerical examples with different crack configurations and boundary conditions are considered. The current approach is validated by comparing the results of dynamic SIFs with available reference solutions. © 2023 Elsevier Ltd