Enlarging the thermal coagulation volume during thermochemical ablation with alternating acid-base injection by shortening the injection interval : a computational study
- Mak, Nguoy, Ng, Wen, Ooi, Ean, Lau, Ee, Pamidi, Narendra, Foo, Ji, Ooi, Ean Tat, Ali, Ahmad
- Authors: Mak, Nguoy , Ng, Wen , Ooi, Ean , Lau, Ee , Pamidi, Narendra , Foo, Ji , Ooi, Ean Tat , Ali, Ahmad
- Date: 2024
- Type: Text , Journal article
- Relation: Computer Methods and Programs in Biomedicine Vol. 243, no. (2024), p.
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- Description: Background and objectives: Thermochemical ablation (TCA) is a cancer treatment that utilises the heat released from the neutralisation of acid and base to raise tissue temperature to levels sufficient to induce thermal coagulation. Computational studies have demonstrated that the coagulation volume produced by sequential injection is smaller than that with simultaneous injection. By injecting the reagents in an ensuing manner, the region of contact between acid and base is limited to a thin contact layer sandwiched between the distribution of acid and base. It is hypothesised that increasing the frequency of acid-base injections into the tissue by shortening the injection interval for each reagent can increase the effective area of contact between acid and base, thereby intensifying neutralisation and the exothermic heat released into the tissue. Methods: To verify this hypothesis, a computational model was developed to simulate the thermochemical processes involved during TCA with sequential injection. Four major processes that take place during TCA were considered, i.e., the flow of acid and base, their neutralisation, the release of exothermic heat and the formation of thermal damage inside the tissue. Equimolar acid and base at 7.5 M was injected into the tissue intermittently. Six injection intervals, namely 3, 6, 15, 20, 30 and 60 s were investigated. Results: Shortening of the injection interval led to the enlargement of coagulation volume. If one considers only the coagulation volume as the determining factor, then a 15 s injection interval was found to be optimum. Conversely, if one places priority on safety, then a 3 s injection interval would result in the lowest amount of reagent residue inside the tissue after treatment. With a 3 s injection interval, the coagulation volume was found to be larger than that of simultaneous injection with the same treatment parameters. Not only that, the volume also surpassed that of radiofrequency ablation (RFA); a conventional thermal ablation technique commonly used for liver cancer treatment. Conclusion: The numerical results verified the hypothesis that shortening the injection interval will lead to the formation of larger thermal coagulation zone during TCA with sequential injection. More importantly, a 3 s injection interval was found to be optimum for both efficacy (large coagulation volume) and safety (least amount of reagent residue). © 2023 The Author(s)
- Authors: Mak, Nguoy , Ng, Wen , Ooi, Ean , Lau, Ee , Pamidi, Narendra , Foo, Ji , Ooi, Ean Tat , Ali, Ahmad
- Date: 2024
- Type: Text , Journal article
- Relation: Computer Methods and Programs in Biomedicine Vol. 243, no. (2024), p.
- Full Text:
- Reviewed:
- Description: Background and objectives: Thermochemical ablation (TCA) is a cancer treatment that utilises the heat released from the neutralisation of acid and base to raise tissue temperature to levels sufficient to induce thermal coagulation. Computational studies have demonstrated that the coagulation volume produced by sequential injection is smaller than that with simultaneous injection. By injecting the reagents in an ensuing manner, the region of contact between acid and base is limited to a thin contact layer sandwiched between the distribution of acid and base. It is hypothesised that increasing the frequency of acid-base injections into the tissue by shortening the injection interval for each reagent can increase the effective area of contact between acid and base, thereby intensifying neutralisation and the exothermic heat released into the tissue. Methods: To verify this hypothesis, a computational model was developed to simulate the thermochemical processes involved during TCA with sequential injection. Four major processes that take place during TCA were considered, i.e., the flow of acid and base, their neutralisation, the release of exothermic heat and the formation of thermal damage inside the tissue. Equimolar acid and base at 7.5 M was injected into the tissue intermittently. Six injection intervals, namely 3, 6, 15, 20, 30 and 60 s were investigated. Results: Shortening of the injection interval led to the enlargement of coagulation volume. If one considers only the coagulation volume as the determining factor, then a 15 s injection interval was found to be optimum. Conversely, if one places priority on safety, then a 3 s injection interval would result in the lowest amount of reagent residue inside the tissue after treatment. With a 3 s injection interval, the coagulation volume was found to be larger than that of simultaneous injection with the same treatment parameters. Not only that, the volume also surpassed that of radiofrequency ablation (RFA); a conventional thermal ablation technique commonly used for liver cancer treatment. Conclusion: The numerical results verified the hypothesis that shortening the injection interval will lead to the formation of larger thermal coagulation zone during TCA with sequential injection. More importantly, a 3 s injection interval was found to be optimum for both efficacy (large coagulation volume) and safety (least amount of reagent residue). © 2023 The Author(s)
Slope stability analysis considering fully saturated poro-elasto-plasticity by an image-based scaled boundary finite element approach
- Wijesinghe, Dakshith, Dyson, Ashley, You, Greg, Khandelwal, Manoj, Natarajan, Sundararajan, Chan, Andrew, Ooi, Ean Tat
- Authors: Wijesinghe, Dakshith , Dyson, Ashley , You, Greg , Khandelwal, Manoj , Natarajan, Sundararajan , Chan, Andrew , Ooi, Ean Tat
- Date: 2024
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 158, no. (2024), p. 160-181
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- Description: Open pit mines are large geotechnical structures. Their stability is an important consideration in the mining industry. The deformations of geotechnical structures often involve the coupled interaction between the pore fluid pressure and the nonlinear deformation of soil, characterised by poro-elasto-plastic behaviour. This paper develops the scaled boundary finite element method (SBFEM) to address poro-elasto-plastic in slope stability problems. It builds upon a previously developed elasto-plastic formulation to consider the effect of pore fluid pressure and its interaction with the nonlinear deformation within the soil. The pore pressure field introduces an additional variable in the governing equations that is similarly discretised using SBFEM shape functions. The SBFEM is implemented together with a pixel-based quadtree mesh generation technique, enabling automatic meshing directly from digital images. This leads to efficient automation when modelling problems with iterative changes in the geometry such as in optimisation of construction processes during the rehabilitation of slopes. The formulation is validated first using a standard numerical benchmark. Application of the developed technique in construction applications in slopes where the stability and effect of pore water pressure is considered e.g., tailings dam construction and optimisation of backfilling process is demonstrated in three examples to demonstrate feasibility. © 2023 The Authors
- Authors: Wijesinghe, Dakshith , Dyson, Ashley , You, Greg , Khandelwal, Manoj , Natarajan, Sundararajan , Chan, Andrew , Ooi, Ean Tat
- Date: 2024
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 158, no. (2024), p. 160-181
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- Description: Open pit mines are large geotechnical structures. Their stability is an important consideration in the mining industry. The deformations of geotechnical structures often involve the coupled interaction between the pore fluid pressure and the nonlinear deformation of soil, characterised by poro-elasto-plastic behaviour. This paper develops the scaled boundary finite element method (SBFEM) to address poro-elasto-plastic in slope stability problems. It builds upon a previously developed elasto-plastic formulation to consider the effect of pore fluid pressure and its interaction with the nonlinear deformation within the soil. The pore pressure field introduces an additional variable in the governing equations that is similarly discretised using SBFEM shape functions. The SBFEM is implemented together with a pixel-based quadtree mesh generation technique, enabling automatic meshing directly from digital images. This leads to efficient automation when modelling problems with iterative changes in the geometry such as in optimisation of construction processes during the rehabilitation of slopes. The formulation is validated first using a standard numerical benchmark. Application of the developed technique in construction applications in slopes where the stability and effect of pore water pressure is considered e.g., tailings dam construction and optimisation of backfilling process is demonstrated in three examples to demonstrate feasibility. © 2023 The Authors
Adaptive phase-field modelling of fracture propagation in poroelastic media using the scaled boundary finite element method
- Wijesinghe, Dakshith, Natarajan, Sundararajan, You, Greg, Khandelwal, Manoj, Dyson, Ashley, Song, Chongmin, Ooi, Ean Tat
- Authors: Wijesinghe, Dakshith , Natarajan, Sundararajan , You, Greg , Khandelwal, Manoj , Dyson, Ashley , Song, Chongmin , Ooi, Ean Tat
- Date: 2023
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 411, no. (2023), p.
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- Description: A scaled boundary finite element-based phase field formulation is proposed to model two-dimensional fracture in saturated poroelastic media. The mechanical response of the poroelastic media is simulated following Biot's theory, and the fracture surface evolution is modelled according to the phase field formulation. To avoid the application of fine uniform meshes that are constrained by the element size requirement when adopting phase field models, an adaptive refinement strategy based on quadtree meshes is adopted. The unique advantage of the scaled boundary finite element method is conducive to the application of quadtree adaptivity, as it can be directly formulated on quadtree meshes without the need for any special treatment of hanging nodes. Efficient computation is achieved by exploiting the unique patterns of the quadtree cells. An appropriate scaling is applied to the relevant matrices and vectors according the physical size of the cells in the mesh during the simulations. This avoids repetitive calculations of cells with the same configurations. The proposed model is validated using a benchmark with a known analytical solution. Numerical examples of hydraulic fractures driven by the injected fluid in cracks are modelled to illustrate the capabilities of the proposed model in handling crack propagation problems involving complex geometries. © 2023 The Author(s)
- Authors: Wijesinghe, Dakshith , Natarajan, Sundararajan , You, Greg , Khandelwal, Manoj , Dyson, Ashley , Song, Chongmin , Ooi, Ean Tat
- Date: 2023
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 411, no. (2023), p.
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- Description: A scaled boundary finite element-based phase field formulation is proposed to model two-dimensional fracture in saturated poroelastic media. The mechanical response of the poroelastic media is simulated following Biot's theory, and the fracture surface evolution is modelled according to the phase field formulation. To avoid the application of fine uniform meshes that are constrained by the element size requirement when adopting phase field models, an adaptive refinement strategy based on quadtree meshes is adopted. The unique advantage of the scaled boundary finite element method is conducive to the application of quadtree adaptivity, as it can be directly formulated on quadtree meshes without the need for any special treatment of hanging nodes. Efficient computation is achieved by exploiting the unique patterns of the quadtree cells. An appropriate scaling is applied to the relevant matrices and vectors according the physical size of the cells in the mesh during the simulations. This avoids repetitive calculations of cells with the same configurations. The proposed model is validated using a benchmark with a known analytical solution. Numerical examples of hydraulic fractures driven by the injected fluid in cracks are modelled to illustrate the capabilities of the proposed model in handling crack propagation problems involving complex geometries. © 2023 The Author(s)
Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation
- Xiao, B., Natarajan, Sundararajan, Birk, Carolin, Ooi, Ean Hin, Song, Chongmin, Ooi, Ean Tat
- Authors: Xiao, B. , Natarajan, Sundararajan , Birk, Carolin , Ooi, Ean Hin , Song, Chongmin , Ooi, Ean Tat
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 124, no. 17 (2023), p. 3603-3636
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- Description: A general technique to develop arbitrary-sided polygonal elements based on the scaled boundary finite element method is presented. Shape functions are derived from the solution of the Poisson's equation in contrast to the well-known Laplace shape functions that are only linearly complete. The application of the Poisson shape functions can be complete up to any specific order. The shape functions retain the advantage of the scaled boundary finite element method allowing direct formulation on polygons with arbitrary number of sides and quadtree meshes. The resulting formulation is similar to the finite element method where each field variable is interpolated by the same set of shape functions in parametric space and differs only in the integration of the stiffness and mass matrices. Well-established finite element procedures can be applied with the developed shape functions, to solve a variety of engineering problems including, for example, coupled field problems, phase field fracture, and addressing volumetric locking in the near-incompressibility limit by adopting a mixed formulation. Application of the formulation is demonstrated in several engineering problems. Optimal convergence rates are observed. © 2023 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
- Authors: Xiao, B. , Natarajan, Sundararajan , Birk, Carolin , Ooi, Ean Hin , Song, Chongmin , Ooi, Ean Tat
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 124, no. 17 (2023), p. 3603-3636
- Full Text:
- Reviewed:
- Description: A general technique to develop arbitrary-sided polygonal elements based on the scaled boundary finite element method is presented. Shape functions are derived from the solution of the Poisson's equation in contrast to the well-known Laplace shape functions that are only linearly complete. The application of the Poisson shape functions can be complete up to any specific order. The shape functions retain the advantage of the scaled boundary finite element method allowing direct formulation on polygons with arbitrary number of sides and quadtree meshes. The resulting formulation is similar to the finite element method where each field variable is interpolated by the same set of shape functions in parametric space and differs only in the integration of the stiffness and mass matrices. Well-established finite element procedures can be applied with the developed shape functions, to solve a variety of engineering problems including, for example, coupled field problems, phase field fracture, and addressing volumetric locking in the near-incompressibility limit by adopting a mixed formulation. Application of the formulation is demonstrated in several engineering problems. Optimal convergence rates are observed. © 2023 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
Modeling cyclic crack propagation in concrete using the scaled boundary finite element method coupled with the cumulative damage-plasticity constitutive law
- Alrayes, Omar, Könke, Carsten, Ooi, Ean Tat, Hamdia, Khader
- Authors: Alrayes, Omar , Könke, Carsten , Ooi, Ean Tat , Hamdia, Khader
- Date: 2023
- Type: Text , Journal article
- Relation: Materials Vol. 16, no. 2 (2023), p.
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- Description: Many concrete structures, such as bridges and wind turbine towers, fail mostly due to the fatigue rapture and bending, where the cracks are initiated and propagate under cyclic loading. Modeling the fracture process zone (FPZ) is essential to understanding the cracking behavior of heterogeneous, quasi-brittle materials such as concrete under monotonic and cyclic actions. The paper aims to present a numerical modeling approach for simulating crack growth using a scaled boundary finite element model (SBFEM). The cohesive traction law is explored to model the stress field under monotonic and cyclic loading conditions. In doing so, a new constitutive law is applied within the cohesive response. The cyclic damage accumulation during loading and unloading is formulated within the thermodynamic framework of the constitutive concrete model. We consider two common problems of three-point bending of a single-edge-notched concrete beam subjected to different loading conditions to validate the developed method. The simulation results show good agreement with experimental test measurements from the literature. The presented analysis can provide a further understanding of crack growth and damage accumulation within the cohesive response, and the SBFEM makes it possible to identify the fracture behavior of cyclic crack propagation in concrete members. © 2023 by the authors.
- Authors: Alrayes, Omar , Könke, Carsten , Ooi, Ean Tat , Hamdia, Khader
- Date: 2023
- Type: Text , Journal article
- Relation: Materials Vol. 16, no. 2 (2023), p.
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- Description: Many concrete structures, such as bridges and wind turbine towers, fail mostly due to the fatigue rapture and bending, where the cracks are initiated and propagate under cyclic loading. Modeling the fracture process zone (FPZ) is essential to understanding the cracking behavior of heterogeneous, quasi-brittle materials such as concrete under monotonic and cyclic actions. The paper aims to present a numerical modeling approach for simulating crack growth using a scaled boundary finite element model (SBFEM). The cohesive traction law is explored to model the stress field under monotonic and cyclic loading conditions. In doing so, a new constitutive law is applied within the cohesive response. The cyclic damage accumulation during loading and unloading is formulated within the thermodynamic framework of the constitutive concrete model. We consider two common problems of three-point bending of a single-edge-notched concrete beam subjected to different loading conditions to validate the developed method. The simulation results show good agreement with experimental test measurements from the literature. The presented analysis can provide a further understanding of crack growth and damage accumulation within the cohesive response, and the SBFEM makes it possible to identify the fracture behavior of cyclic crack propagation in concrete members. © 2023 by the authors.
Communication-a-fast and accurate numerical technique for impedance spectroscopy of microstructures
- Swaminathan, Narasimhan, Natarajan, Sundararajan, Ooi, Ean Tat
- Authors: Swaminathan, Narasimhan , Natarajan, Sundararajan , Ooi, Ean Tat
- Date: 2022
- Type: Text , Journal article
- Relation: Journal of the Electrochemical Society Vol. 169, no. 2 (2022), p.
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- Description: The polygonal finite element method (PFEM) is proposed as a fast and accurate technique to simulate the impedance spectroscopy (IS) of polycrystalline materials. While conventional finite element method (FEM) requires explicit meshing of the grains and grain boundaries, in PFEM each region can be treated as an element. We demonstrate that the number of degrees of freedom in PFEM can be lower by a factor of 30 when compared to FEM, thus speeding up simulations by a factor of 3.5. A simple example demonstrates the use of PFEM to generate IS on samples with various grain boundary widths. © 2022 The Author(s).
- Authors: Swaminathan, Narasimhan , Natarajan, Sundararajan , Ooi, Ean Tat
- Date: 2022
- Type: Text , Journal article
- Relation: Journal of the Electrochemical Society Vol. 169, no. 2 (2022), p.
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- Description: The polygonal finite element method (PFEM) is proposed as a fast and accurate technique to simulate the impedance spectroscopy (IS) of polycrystalline materials. While conventional finite element method (FEM) requires explicit meshing of the grains and grain boundaries, in PFEM each region can be treated as an element. We demonstrate that the number of degrees of freedom in PFEM can be lower by a factor of 30 when compared to FEM, thus speeding up simulations by a factor of 3.5. A simple example demonstrates the use of PFEM to generate IS on samples with various grain boundary widths. © 2022 The Author(s).
A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete
- Guo, H., Ooi, Ean Tat, Saputra, Albert, Yang, Zhenjun, Natarajan, Sundararajan, Ooi, Ean Hin, Song, Chongmin
- 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
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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.
- 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:
- Reviewed:
- 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.
A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics
- Song, Chongmin, Ooi, Ean Tat, Natarajan, Sundararajan
- 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
- 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
- Full Text:
- Reviewed:
- 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
A scaled boundary finite element formulation with bubble functions for elasto-static analyses of functionally graded materials
- Ooi, Ean Tat, Song, Chongmin, Natarajan, Sundararajan
- Authors: Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2017
- Type: Text , Journal article
- Relation: Computational Mechanics Vol. 60, no. 6 (2017), p. 943-967
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- Description: This manuscript presents an extension of the recently-developed high order complete scaled boundary shape functions to model elasto-static problems in functionally graded materials. Both isotropic and orthotropic functionally graded materials are modelled. The high order complete properties of the shape functions are realized through the introduction of bubble-like functions derived from the equilibrium condition of a polygon subjected to body loads. The bubble functions preserve the displacement compatibility between the elements in the mesh. The heterogeneity resulting from the material gradient introduces additional terms in the polygon stiffness matrix that are integrated analytically. Few numerical benchmarks were used to validate the developed formulation. The high order completeness property of the bubble functions result in superior accuracy and convergence rates for generic elasto-static and fracture problems involving functionally graded materials. © 2017, Springer-Verlag GmbH Germany.
- Authors: Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2017
- Type: Text , Journal article
- Relation: Computational Mechanics Vol. 60, no. 6 (2017), p. 943-967
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- Description: This manuscript presents an extension of the recently-developed high order complete scaled boundary shape functions to model elasto-static problems in functionally graded materials. Both isotropic and orthotropic functionally graded materials are modelled. The high order complete properties of the shape functions are realized through the introduction of bubble-like functions derived from the equilibrium condition of a polygon subjected to body loads. The bubble functions preserve the displacement compatibility between the elements in the mesh. The heterogeneity resulting from the material gradient introduces additional terms in the polygon stiffness matrix that are integrated analytically. Few numerical benchmarks were used to validate the developed formulation. The high order completeness property of the bubble functions result in superior accuracy and convergence rates for generic elasto-static and fracture problems involving functionally graded materials. © 2017, Springer-Verlag GmbH Germany.
Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling
- Ooi, Ean Tat, Man, Hou, Natarajan, Sundararajan, Song, Chongmin
- 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.
- 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.
A quadtree-based scaled boundary finite element method for crack propagation modelling
- Ooi, Ean Tat, Man, Hou, Natarajan, Sundararajan, Song, Chongmin, Tin-Loi, Francis
- 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
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- 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.
- 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.
A scaled boundary polygon formulation for elasto-plastic analyses
- Ooi, Ean Tat, Song, Chongmin, Tin-Loi, Francis
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 268, no. (January 2014 2014), p. 905-937
- Full Text:
- Reviewed:
- Description: This study presents a novel scaled boundary polygon formulation to model elasto-plastic material responses in structures. The polygons have flexible mesh generation capabilities and are more accurate than standard finite elements, especially for problems with cracks and notches. Shape functions of arbitrary n-sided polygons are constructed using the scaled boundary finite element method. These shape functions are conforming and linearly complete. When modeling a crack, strain singularities are analytically modeled without enrichment. Standard finite element procedures are used to formulate the stiffness matrix and residual load vector. The nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function. The stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present. Standard nonlinear equation solvers e.g. the modified Newton–Raphson algorithm are used to obtain the nonlinear response of the structure. The proposed formulation is validated using several numerical benchmarks.
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 268, no. (January 2014 2014), p. 905-937
- Full Text:
- Reviewed:
- Description: This study presents a novel scaled boundary polygon formulation to model elasto-plastic material responses in structures. The polygons have flexible mesh generation capabilities and are more accurate than standard finite elements, especially for problems with cracks and notches. Shape functions of arbitrary n-sided polygons are constructed using the scaled boundary finite element method. These shape functions are conforming and linearly complete. When modeling a crack, strain singularities are analytically modeled without enrichment. Standard finite element procedures are used to formulate the stiffness matrix and residual load vector. The nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function. The stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present. Standard nonlinear equation solvers e.g. the modified Newton–Raphson algorithm are used to obtain the nonlinear response of the structure. The proposed formulation is validated using several numerical benchmarks.
Experimental and numerical study of the dependency of interface fracture in concrete–rock specimens on mode mixity
- Zhong, Hong, Ooi, Ean Tat, Song, Chongmin, Ding, Tao, Lin, Gao, Li, Hongjun
- Authors: Zhong, Hong , Ooi, Ean Tat , Song, Chongmin , Ding, Tao , Lin, Gao , Li, Hongjun
- Date: 2014
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol.124-125, no. (2014), p. 287-309
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- Reviewed:
- Authors: Zhong, Hong , Ooi, Ean Tat , Song, Chongmin , Ding, Tao , Lin, Gao , Li, Hongjun
- Date: 2014
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol.124-125, no. (2014), p. 287-309
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- Reviewed:
Finite element computations over quadtree meshes : Strain smoothing and semi-analytical formulation
- Natarajan, Sundararajan, Ooi, Ean Tat, Song, Chongmin
- Authors: Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin
- Date: 2013
- Type: Text , Journal article
- Relation: International Journal of Advances in Engineering Sciences and Applied Mathematics Vol. 7, no. 3 (2013), p. 124-133
- Full Text:
- Reviewed:
- Description: In this paper, we discuss two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form of the shape functions, unlike the conventional approaches, for example, as in the work of Gupta (Int J Numer Methods Eng 12:35, 1978) or Tabarraei and Sukumar (Finite Elem Anal Des 41:686, 2005). Hence, no special numerical integration technique is required. One of the techniques relies on the strain projection procedure, whilst the other is based on the scaled boundary finite element method. Numerical examples are presented to demonstrate the accuracy and the convergence properties of the two techniques.
- Authors: Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin
- Date: 2013
- Type: Text , Journal article
- Relation: International Journal of Advances in Engineering Sciences and Applied Mathematics Vol. 7, no. 3 (2013), p. 124-133
- Full Text:
- Reviewed:
- Description: In this paper, we discuss two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form of the shape functions, unlike the conventional approaches, for example, as in the work of Gupta (Int J Numer Methods Eng 12:35, 1978) or Tabarraei and Sukumar (Finite Elem Anal Des 41:686, 2005). Hence, no special numerical integration technique is required. One of the techniques relies on the strain projection procedure, whilst the other is based on the scaled boundary finite element method. Numerical examples are presented to demonstrate the accuracy and the convergence properties of the two techniques.
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