Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons
- Authors: Chiong, Irene , Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 131, no. (2014), p. 210-231
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- Description: In this paper, the recently developed scaled boundary polygons formulation for the evaluation of stress intensity factors in functionally graded materials is extended to elasto-dynamics. In this approach, the domain is discretized using polygons with arbitrary number of sides. Within each polygon, the scaled boundary polygon shape functions are used to interpolate the displacement field. For uncracked polygons, these shape functions are linearly complete. In a cracked polygon, the shape functions analytically model the stress singularity at the crack tip. Therefore, accurate dynamic stress intensity factors can be computed directly from their definitions. Only a single polygon is necessary to accurately compute the stress intensity factors. To model the material heterogeneity in functionally graded materials, the material gradients are approximated locally in each polygon using polynomial functions. This leads to semi-analytical expressions for both the stiffness and the mass matrices, which can be integrated straightforwardly. The versatility of the developed formulation is demonstrated by modeling five numerical examples involving cracked functionally graded specimens subjected to dynamic loads. © 2014 Elsevier Ltd.
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
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- 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.
Scaled boundary polygons with application to fracture analysis of functionally graded materials
- Authors: Chiong, Irene , Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 98, no. (2014), p.562-589
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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
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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.
Evaluation of stress intensity factors on cracked functionally graded materials using polygons modelled by the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Chiong, Irene , Song, Chongmin
- Date: 2013
- Type: Text , Conference proceedings
- Relation: 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 2012; Sydney, NSW; Australia; 11th-14th Dec, 2012 published in From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM p. 201-206
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- Description: Functionally graded materials are a relatively newclass of composite materialswhere its material properties are defined by a continuous function on the spatial coordinates. Its use in engineering practice is increasingly popular due to its superior mechanical and thermo-mechanical properties. Understanding the behaviour of cracks in functionally graded materials is important in the assessment of their structural integrity. This study develops a novel approach using polygon elements, which are modelled by the scaled boundary finite element method, to analyse the fracture behaviour in functionally graded materials. The scaled boundary finite element equations are reformulated in terms of nodal shape functions. Each polygon is then treated using standard finite element procedures. The non-uniform material properties are locally represented by a polynomial fit in the element formulation. This formulation still inherits all the advantages of the scaled boundary finite element method. Orders of singularities and hence, stress intensity factors can be computed accurately using only singular modes in the scaled boundary finite element solution without nodal enrichment functions. Mesh refinement at the crack tip is significantly less compared to that required in standard finite element method and is only necessary to model the graded material properties throughout the computational domain. The efficiency of the method in evaluating stress intensity factors are demonstrated using a few numerical examples. © 2013 Taylor & Francis Group.
- Description: From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 2012
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-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
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- 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
Crack propagation modeling in functionally graded materials using polygon elements modeled by the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Guo, ShuHong , Song, Chongmin
- Date: 2013
- Type: Text , Conference proceedings
- Relation: 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 2012; Sydney, NSW; Australia; 11th-14th December 2012; Published in From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM p. 133-138
- Full Text: false
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- Description: Functionally graded materials (FGMs) are multi-phased composites that are specifically engineered so that their material properties vary continuously in a predetermined direction. The heterogeneity in FGMs results in superior fracture resistance, making them suitable for use as medical implants and components in nuclear, aerospace and electro-mechanical industries. The degree to which the fracture resistance of FGMs can be improved is usually not known a priori. Understanding their fracture behaviour provides insights to design better FGMs and enables quantitative assessment of the structural integrity in manufactured FGM products. A novel methodology is developed in this study to model crack propagation in FGMs. It uses high order polygon elements that are modelled by the scaled boundary finite element method. The displacement and stress fields in each polygon are expressed using scaled boundary shape functions and corresponding nodal displacements. Material heterogeneity is modelled by locally fitting a polynomial curve in terms of scaled boundary finite element coordinates over each polygon. The developed method is very efficient in modelling singular stress fields in the vicinity of cracks. Stress intensity factors are evaluated directly from the singular modes in the scaled boundary finite element solutions to determine the crack propagation direction.A simple local remeshing algorithm for polygons is developed to accommodate crack propagation. Fracture analyses of FGMs are conducted on three numerical examples to validate the methodology and demonstrate its salient features. Fracture parameters e.g. stress intensity factors, critical failure load and crack propagation paths of FGM specimens can be obtained from these analyses. © 2013 Taylor & Francis Group.
- Description: From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 2012