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
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- 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.
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
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- 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.
A dual scaled boundary finite element formulation over arbitrary faceted star convex polyhedra
- Authors: Ooi, Ean Tat , Saputra, Albert , Natarajan, Sundararajan , Ooi, Ean Hin , Song, Chongmin
- Date: 2020
- Type: Text , Journal article
- Relation: Computational Mechanics Vol. 66, no. 1 (2020), p. 27-47
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- Description: A novel technique to formulate arbritrary faceted polyhedral elements in three-dimensions is presented. The formulation is applicable for arbitrary faceted polyhedra, provided that a scaling requirement is satisfied and the polyhedron facets are planar. A triangulation process can be applied to non-planar facets to generate an admissible geometry. The formulation adopts two separate scaled boundary coordinate systems with respect to: (i) a scaling centre located within a polyhedron and; (ii) a scaling centre on a polyhedron’s facets. The polyhedron geometry is scaled with respect to both the scaling centres. Polygonal shape functions are derived using the scaled boundary finite element method on the polyhedron facets. The stiffness matrix of a polyhedron is obtained semi-analytically. Numerical integration is required only for the line elements that discretise the polyhedron boundaries. The new formulation passes the patch test. Application of the new formulation in computational solid mechanics is demonstrated using a few numerical benchmarks. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
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
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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.
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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
Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation
- 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.