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:
- 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.
Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method
- Authors: Hirshikesh , Pramod, Aladurthi , Annabattula, Ratna , Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2019
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 355, no. (2019), p. 284-307
- Full Text: false
- Reviewed:
- Description: In this work, we propose an adaptive phase field method (PFM) to simulate quasi-static brittle fracture problems. The phase field equations are solved using the scaled boundary finite element method (SBFEM). The adaptive refinement strategy is based on an error indicator evaluated directly from the solutions of the SBFEM without any need for stress recovery techniques. Quadtree meshes are adapted to perform mesh refinement. The polygons with hanging nodes in the quadtree decomposition are treated as n−sided polygons within the framework of the SBFEM and do not require any special treatment in contrast to the conventional finite element method. Several benchmark problems are used to demonstrate the robustness and the efficacy of the proposed technique. The adaptive refinement strategy reduces the mesh burden when adopting the PFM to model fracture. Numerical results show an improvement in the computational efficiency in terms of the number of elements required in the standard PFM without compromising the accuracy of the solution.
Scaled boundary finite element method for compressible and nearly incompressible elasticity over arbitrary polytopes
- Authors: Aladurthi, Lakshmi , Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin
- Date: 2019
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 119, no. 13 (2019), p. 1379-1394
- Full Text: false
- Reviewed:
- Description: In this paper, a purely displacement-based formulation is presented within the framework of the scaled boundary finite element method to model compressible and nearly incompressible materials. A selective reduced integration technique combined with an analytical treatment in the nearly incompressible limit is employed to alleviate volumetric locking. The stiffness matrix is computed by solving the scaled boundary finite element equation. The salient feature of the proposed technique is that it neither requires a stabilization parameter nor adds additional degrees of freedom to handle volumetric locking. The efficiency and the robustness of the proposed approach is demonstrated by solving various numerical examples in two and three dimensions.
The effects of electrical and thermal boundary condition on the simulation of radiofrequency ablation of liver cancer for tumours located near to the liver boundary
- Authors: Ooi, Ean Hin , Lee, Khiy , Yap, Shelley , Khattab, Mahmoud , Liao, Iman , Ooi, Ean Tat , Foo, Ji , Nair, Shalini , Ali, Ahmad
- Date: 2019
- Type: Text , Journal article
- Relation: Computers in Biology and Medicine Vol. 106, no. (2019), p. 12-23
- Full Text: false
- Reviewed:
- Description: Effects of different boundary conditions prescribed across the boundaries of radiofrequency ablation (RFA) models of liver cancer are investigated for the case where the tumour is at the liver boundary. Ground and Robin-type conditions (electrical field) and body temperature and thermal insulation (thermal field) conditions are examined. 3D models of the human liver based on publicly-available CT images of the liver are developed. An artificial tumour is placed inside the liver at the boundary. Simulations are carried out using the finite element method. The numerical results indicated that different electrical and thermal boundary conditions led to different predictions of the electrical potential, temperature and thermal coagulation distributions. Ground and body temperature conditions presented an unnatural physical conditions around the ablation site, which results in more intense Joule heating and excessive heat loss from the tissue. This led to thermal damage volumes that are smaller than the cases when the Robin type or the thermal insulation conditions are prescribed. The present study suggests that RFA simulations in the future must take into consideration the choice of the type of electrical and thermal boundary conditions to be prescribed in the case where the tumour is located near to the liver boundary.
A novel error indicator and an adaptive refinement technique using the scaled boundary finite element method
- Authors: Song, Chongmin , Ooi, Ean Tat , Pramod, Aladurthi , Natarajan, Sundararajan
- Date: 2018
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 94, no. (2018), p. 10-24
- Full Text: false
- Reviewed:
- Description: In this paper, an adaptive refinement strategy based on the scaled boundary finite element method on quadtree meshes for linear elasticity problems is discussed. Within this framework, the elements with hanging nodes are treated as polygonal elements and thus does not require special treatment. The adaptive refinement is supplemented with a novel error indicator. The local error is estimated directly from the solution of the scaled boundary governing equations. The salient feature is that it does not require any stress recovery techniques. The efficacy and the robustness of the proposed approach are demonstrated with a few numerical examples.
A novel scaled boundary finite element formulation with stabilization and its application to image-based elastoplastic analysis
- Authors: He, Ke , Song, Chongmin , Ooi, Ean Tat
- Date: 2018
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 115, no. 8 (2018), p. 956-985
- Full Text: false
- Reviewed:
- Description: Digital images are increasingly being used as input data for computational analyses. This study presents an efficient numerical technique to perform image-based elastoplastic analysis of materials and structures. The quadtree decomposition algorithm is employed for image-based mesh generation, which is fully automatic and highly efficient. The quadtree cells are modeled by scaled boundary polytope elements, which eliminate the issue of hanging nodes faced by standard finite elements. A novel, simple, and efficient scaled boundary elastoplastic formulation with stablisation is developed. In this formulation, the return-mapping calculation is only required to be performed at a single point in a polytope element, which facilitates the computational efficiency of the elastoplastic analysis and simplicity of implementation. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed technique for performing the elastoplastic analysis of high-resolution images.
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 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
- 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
Comparison between single- and dual-porosity models for fluid transport in predicting lesion volume following saline-infused radiofrequency ablation
- Authors: Ooi, Ean Hin , Chia, Nicholas , Ooi, Ean Tat , Foo, Ji , Liao, Imam , Nair, Shalini , Mohd Ali, Ahmad
- Date: 2018
- Type: Text , Journal article
- Relation: International Journal of Hyperthermia Vol. 34, no. 8 (2018), p. 1142-1156
- Full Text: false
- Reviewed:
- Description: A recent study by Ooi and Ooi (EH Ooi, ET Ooi, Mass transport in biological tissues: Comparisons between single- and dual-porosity models in the context of saline-infused radiofrequency ablation, Applied Mathematical Modelling, 2017, 41, 271-284) has shown that single-porosity (SP) models for describing fluid transport in biological tissues significantly underestimate the fluid penetration depth when compared to dual-porosity (DP) models. This has raised some concerns on whether the SP model, when coupled with models of radiofrequency ablation (RFA) to simulate saline-infused RFA, could lead to an underestimation of the coagulation size. This paper compares the coagulation volumes obtained following saline-infused RFA predicted based on the SP and DP models for fluid transport. Results showed that the SP model predicted coagulation zones that are consistently 0.5 to 0.9 times smaller than that of DP model. This may be explained by the low permeability value of the tissue interstitial space, which causes the majority of the saline to flow through the vasculature. The absence of fluid flow tracking in the vasculature in the SP model meant that any flow of saline into the vasculature is treated as losses and do not contribute to the saline penetration depth of the tissue. Comparisons with experimental results from the literature revealed that the DP models predicted coagulation zone sizes that are closer to the experimental values than the SP models. This supports the hypothesis that the SP model is a poor choice for simulating the outcome of saline-infused RFA.
Hydraulic fracture at the dam-foundation interface using the scaled boundary finite element method coupled with the cohesive crack model
- Authors: Zhong, Hong , Li, Hongjun , Ooi, Ean Tat , Song, Chongmin
- Date: 2018
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 88, no. (2018), p. 41-53
- Full Text: false
- Reviewed:
- Description: The scaled boundary finite element method coupled with the cohesive crack model is extended to investigate the hydraulic fracture at the dam-foundation interface. The concrete and rock bulk are modeled by the scaled boundary polygons. Cohesive interface elements model the fracture process zone between the crack faces. The cohesive tractions are modeled as side-face tractions in the scaled boundary polygons. The solution of the stress field around the crack tip is expressed semi-analytically as a power series. Accurate displacement field, stress field and stress intensity factors can be obtained without asymptotic enrichment or local mesh refinement. The proposed procedure is verified by the hydraulic fracture of a rectangular embankment on rigid foundation and applied to the modeling of hydraulic fracture on the dam-foundation interface of a benchmark dam. Different distributions of water pressure inside the crack are investigated. It is found that the water pressure inside the crack decreases the peak overflow to less than 20% of the case without water in the crack. Considering the water lag or not is significant to the response, while different distribution of pressure following the water lag region in the fracture process zone has negligible influence.
Numerical estimation of stress intensity factors in cracked functionally graded piezoelectric materials - a scaled boundary finite element approach
- Authors: Pramod, A. , Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2018
- Type: Text , Journal article
- Relation: Composite Structures Vol. 206, no. (2018), p. 301-312
- Full Text: false
- Reviewed:
- Description: The stress intensity factors and the electrical displacement intensity factor for functionally graded piezoelectric materials (FGPMs) are influenced by: (a) the spatial variation of the mechanical property and (b) the electrical and mechanical boundary conditions. In this work, a semi-analytical technique is proposed to study the fracture parameters of FGPMs subjected to far field traction and electrical boundary conditions. A scaled boundary finite element formulation for the analysis of functionally graded piezoelectric materials is developed. The formulation is linearly complete for uncracked polygons and can capture crack tip singularity for cracked polygons. These salient features enable the computation of the fracture parameters directly from their definition. Numerical examples involving cracks in FGPMs show the accuracy and efficiency of the proposed technique.
A 2-D polygon discrete element method and program for simulating rockfill materials
- Authors: Luo, Tao , Ooi, Ean Tat , Chan, Andrew , Fu, Shaojun
- Date: 2017
- Type: Text , Journal article
- Relation: Yantu Lixue/Rock and Soil Mechanics Vol. 38, no. 3 (2017), p. 883-892
- Full Text: false
- Reviewed:
- Description: Every single particle is simulated by a polygon discrete element to capture the realistic shape of rockfill materials. A polygon discrete element method (PDEM) is developed by adopting a simple contact detection program and a polygon/polygon contact model. A linear program is adopted to detect the contact details between polygons. Then the normal contact force is calculated by a potential energy based polygon/polygon normal contact model, and a polygon discrete element calculation method is formed. Based on this method, a program called PDEM is developed to study the interaction between particles and both the translational and rotational motion of every particle from the microscopic view. The effect of micro-properties (e.g. particle shape, size, material properties et al.) on the macro-strength and deformation is enabled. A two-dimensional model test of a coarse aggregate was carried out by PDEM program. The stress and deformation laws consistent with the lab experiment were obtained, and the method and procedure were used to study the effectiveness of the rockfill. © 2017, Science Press. All right reserved.
A combined DEM-SBFEM for modelling particle breakage of rock-fill materials
- Authors: Luo, Tao , Ooi, Ean Tat , Chan, Andrew , Fu, Shaojun
- Date: 2017
- Type: Journal article
- Relation: Yantu Lixue/Rock and Soil Mechanics Vol. 38, no. 5 (2017), p. 1463-1471
- Full Text: false
- Reviewed:
- Description: Both experimental and numerical results demonstrate that particle breakage has significant influence on the macro mechanical response of granular soils. In this study, a novel computational method was proposed to simulate particle breakage phenomenon in granular soils. The proposed method based on the discrete element method (DEM) and the scaled boundary finite element method (SBFEM) has advantages of each method. Individual grains of soil are modelled by a single star-convex polygon with an arbitrary number of sides. The DEM is used to determine the motion of particles and the interaction among particles, whereas the SBFEM is applied to obtain stress states of grains at the end of each time step. Since the SBFEM flexibly describes the morphology of each grain with a single polygon consisting of an arbitrary number of sides, it greatly reduces the necessary computational resources for stress analysis. When the stress state has been confirmed, Hoek-Brown criterion is chosen to determine the 'plastic points' within each particle. Once the ratio of 'plastic points' reaches a predefined threshold, the particle breakage is triggered. As a straight breakage line is assumed for simplification, the particle is split into two when breakage occurs. The newly generated polygons are directly modelled by the DEM and SBFEM without any change of the formulation, and thus this method does not need to predefine sub-particles and re-meshing elements. At last, the feasibility of the newly developed method is verified by a biaxial benchmark test. © 2017, Science Press. All right reserved.
A scaled boundary finite element formulation over arbitrary faceted star convex polyhedra
- Authors: Natarajan, Sundararajan , Ooi, Ean Tat , Saputra, Albert , Song, Chongmin
- Date: 2017
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 80, no. (2017), p. 218-229
- Full Text: false
- Reviewed:
- Description: In this paper, a displacement based finite element framework for general three-dimensional convex polyhedra is presented. The method is based on a semi-analytical framework, the scaled boundary finite element method. The method relies on the definition of a scaling center from which the entire boundary is visible. The salient feature of the method is that the discretizations are restricted to the surfaces of the polyhedron, thus reducing the dimensionality of the problem by one. Hence, an explicit form of the shape functions inside the polyhedron is not required. Conforming shape functions defined over arbitrary polygon, such as the Wachpress interpolants are used over each surface of the polyhedron. Analytical integration is employed within the polyhedron. The proposed method passes patch test to machine precision. The convergence and the accuracy properties of the method is discussed by solving few benchmark problems in linear elasticity. © 2017 Elsevier Ltd
A scaled boundary finite element formulation with bubble functions for elasto-static analyses of functionally graded materials
- 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
- Full Text:
- Reviewed:
- 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.
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.
Investigating performance of stormwater filters under controlled and uncontrolled environments
- Authors: Meade, Ben , Heyne, Marcus , Li, Lianggang , Jackson, Daniel , Ooi, Ean Tat , Lee, Lisa , Costa, Susanga , Kandra, Harpreet
- Date: 2017
- Type: Text , Conference paper
- Relation: International Conference On Sustainable Civil Engineering Practices
- Full Text: false
- Reviewed:
- Description: Hydraulic performance and its evolution over time is a key design parameter for stormwater filter systems. The major impact affecting stormwater filters is the reduction in infiltration rate, or otherwise known as clogging. This paper focuses on the effect of biological clogging of non-vegetated high flow stormwater filters in Australian conditions. An experimental column study was undertaken. Five semi-synthetic stormwater dosing configurations were tested: (i) Typical stormwater (base), (ii) Stormwater with high nutrient load, (iii) Typical stormwater with chlorine tablets, (iv) sterilized stormwater, and (v) potable water. Each configuration had 6 replicate columns, 3 were placed inside under controlled laboratory conditions and 3 were placed outside under normal Australian spring weather conditions, except for the potable water case (v) where it only had 2 replicate columns and both were placed outside. The results found were inconclusive due to the insignificant reduction of the infiltration rate over time and the columns did not clog, which is due to the size of sediment used in this study. It is suggested that further work should be undertaken on investigating the effect of stormwater composition in stormwater filters in real world conditions.
The combined scaled boundary finite-discrete element method : Grain breakage modelling in cohesion-less granular media
- Authors: Luo, Tao , Ooi, Ean Tat , Chan, Andrew , Fu, Shaojun
- Date: 2017
- Type: Text , Journal article
- Relation: Computers and Geotechnics Vol. 88, no. (2017), p. 199-221
- Full Text: false
- Reviewed:
- Description: A computational technique combining the scaled boundary finite element method (SBFEM) and the discrete element method (DEM) is developed. Both methodologies work in tandem to model two mechanisms i.e. grain-to-grain interaction via DEM; and breakage of individual grains via SBFEM. Both play important roles in characterising the response of granular soils. The combination of the two methods results in some advantages in computational flexibility and implementation in modelling grain breakage in granular materials. Parametric studies demonstrate the method's ability to reproduce stress-strain curves in bi-axial tests of granular rock-fills; and qualitatively predicts characteristics of grain breakage observed in laboratory tests. © 2017 Elsevier Ltd
Construction of high-order complete scaled boundary shape functions over arbitrary polygons with bubble functions
- Authors: Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2016
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 108, no. 9 (2016), p. 1086-1120
- Full Text: false
- Reviewed:
- Description: This manuscript presents the development of novel high-order complete shape functions over star-convex polygons based on the scaled boundary finite element method. The boundary of a polygon is discretised using one-dimensional high order shape functions. Within the domain, the shape functions are analytically formulated from the equilibrium conditions of a polygon. These standard scaled boundary shape functions are augmented by introducing additional bubble functions, which renders them high-order complete up to the order of the line elements on the polygon boundary. The bubble functions are also semi-analytical and preserve the displacement compatibility between adjacent polygons. They are derived from the scaled boundary formulation by incorporating body force modes. Higher-order interpolations can be conveniently formulated by simultaneously increasing the order of the shape functions on the polygon boundary and the order of the body force mode. The resulting stiffness-matrices and mass-matrices are integrated numerically along the boundary using standard integration rules and analytically along the radial coordinate within the domain. The bubble functions improve the convergence rate of the scaled boundary finite element method in modal analyses and for problems with non-zero body forces. Numerical examples demonstrate the accuracy and convergence of the developed approach. Copyright (c) 2016 John Wiley & Sons, Ltd.
Dynamic fracture simulations using the scaled boundary finite element method on hybrid polygon-quadtree meshes
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Ooi, Ean Hin
- Date: 2016
- Type: Text , Journal article
- Relation: International Journal of Impact Engineering Vol. 90, no. (2016), p. 154-164
- Full Text: false
- Reviewed:
- Description: In this paper, we present an efficient computational procedure to model dynamic fracture within the framework of the scaled boundary finite element method (SBFEM). A quadtree data structure is used to discretise the domain, and 2:1 ratio between the cells is maintained. This limits the number of patterns in the quadtree decomposition and allows for efficient computation of the system matrices. The regions close to the boundary are discretised with arbitrary sided polygons so as to facilitate accurate modelling of the curved boundaries. The stiffness and the mass matrix over all the cells are computed by the SBFEM. Moreover, the semi-analytical nature of the SBFEM enables accurate modelling of the asymptotic stress fields in the vicinity of the crack tip. An efficient remeshing algorithm that combines the quadtree decomposition with simple Boolean operations is proposed to model the crack propagation. The remeshing is restricted only to a small region in the vicinity of the crack tip. The efficiency and the convergence properties of the proposed framework are demonstrated with a few benchmark problems. © 2015 Elsevier Ltd. All rights reserved.