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Application of scaled boundary finite element method for delamination analysis of composite laminates using cohesive zone modelling

- Garg, Nikhil, Prusty, Gangadhara, Ooi, Ean Tat, Song, Chongmin, Pearce, Garth, Phillips, Andrew

  • Authors: Garg, Nikhil , Prusty, Gangadhara , Ooi, Ean Tat , Song, Chongmin , Pearce, Garth , Phillips, Andrew
  • Date: 2020
  • Type: Text , Journal article
  • Relation: Composite Structures Vol. 253, no. (2020), p. 1-10
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  • Description: In this paper, the scaled boundary finite element method (SBFEM) is evaluated for two-dimensional delamination analysis of composite laminates. The delamination phenomenon was studied using cohesive zone modelling (CZM). A bi-linear (triangular) traction-separation law was used to describe the interface behaviour, which was modelled using zero-thickness interface elements. Local arc-length solution technique was used to solve the non-linearity due to the interface behaviour. In this research, pure Mode I and Mode II as well as mixed mode delamination studies have been conducted using the SBFEM formulation. A variety of numerical experiments were performed. Good agreement was observed between the SBFEM simulation and the available numerical and experimental results in the open literature. A comparison between the SBFEM and other traditional methods shows that the presented formulation can solve the same physical problem with a reduction in the computational cost by more than half. The study highlights the advantages of SBFEM over other methods for modelling delamination in composite laminates using CZM.
  • Description: This project is conducted within the ARC Training Centre for Automated Manufacture of Advanced Composites (IC160100040), supported by the Commonwealth of Australia under the Australian Research Council's Industrial Transformation Research Program.

The effects of the no-touch gap on the no-touch bipolar radiofrequency ablation treatment of liver cancer : a numerical study using a two compartment model

- Yap, Shelley, Cheong, Jason, Foo, Ji, Ooi, Ean Tat, Ooi, Ean Hin

  • Authors: Yap, Shelley , Cheong, Jason , Foo, Ji , Ooi, Ean Tat , Ooi, Ean Hin
  • Date: 2020
  • Type: Text , Journal article
  • Relation: Applied Mathematical Modelling Vol. 78, no. (2020), p. 134-147
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  • Description: The no-touch bipolar radiofrequency ablation (RFA) for cancer treatment is advantageous primarily because of its capability to prevent tumour track seeding (TTS). In this technique, the RF probes are placed at a distance (no-touch gap) away from the tumour boundary. Ideally, the RF probes should be placed sufficiently far from the tumour in order to avoid TTS. However, having a gap that is too large can lead to ineffective ablation. This paper investigates how the selection of the no-touch gap can affect the tissue electrical and thermal responses during the no-touch bipolar RFA treatment. Simulations were carried out on a two compartment model using the finite element method. Results obtained indicated that a gap that is too large may lead to incomplete ablation and failure to achieve significant ablation margin. However, keeping the gap to be too small may not be clinically practical. It was suggested that the incomplete ablation and the insufficient ablation margin observed in some of the cases may require the placement of additional probes around the tumour. The present study stresses on the importance of identifying the optimal no-touch gap that can avoid TTS without compromising the treatment outcome. © 2019 Elsevier Inc.

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
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  • 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

Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons

- Chiong, Irene, Ooi, Ean Tat, Song, Chongmin, Tin-Loi, Francis

  • 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.

Convergence and accuracy of displacement based finite element formulations over arbitrary polygons: Laplace interpolants, strain smoothing and scaled boundary polygon formulation

- Natarajan, Sundararajan, Ooi, Ean Tat, Chiong, Irene, Song, Chongmin

  • Authors: Natarajan, Sundararajan , Ooi, Ean Tat , Chiong, Irene , Song, Chongmin
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Finite Elements in Analysis and Design Vol. 85, no. (August 2014 2014), p. 101-122
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  • Description: Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are the conventional polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed polygonal FEM with simple averaging technique and the scaled boundary polygon formulation. For the purpose of numerical integration, we employ the sub-triangulation for polygonal FEM and classical Gaussian quadrature for the smoothed FEM and the scaled boundary polygon formulation. The accuracy and the convergence properties of these formulations are studied with a few benchmark problems in the context of linear elasticity and the linear elastic fracture mechanics. The extension of scaled boundary polygon to higher order polygons is also discussed.

SBFEM for fracture analysis of piezoelectric composites under thermal load

- Li, Chao, Ooi, Ean Tat, Song, Chongmin, Natarajan, Sundararajan

  • Authors: Li, Chao , Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
  • Date: 2015
  • Type: Text , Journal article
  • Relation: International Journal of Solids and Structures Vol. 52, no. 1 (2015), p. 114-129
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  • Description: This paper extends a semi-analytical technique, the so-called scaled boundary finite element method (SBFEM), to analyze fracture behaviors of piezoelectric materials and piezoelectric composites under thermal loading. In this method, only the boundary is discretized leading to a reduction of the spatial dimension by one. The temperature field in the domain is obtained using the SBFEM and expressed as a series of power functions of the radial coordinate. The resulting stress and electric displacement distribution along the radial direction is represented analytically. This permits the generalized stress and electric displacement intensity factors to be directly evaluated from the solution by following standard stress recovery procedures in the finite element method (FEM). Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique. © 2014 Elsevier Ltd.

2D dynamic analysis of cracks and interface cracks in piezoelectric composites using the SBFEM

- Li, Chao, Song, Chongmin, Man, Hou, Ooi, Ean Tat, Gao, Wei

  • Authors: Li, Chao , Song, Chongmin , Man, Hou , Ooi, Ean Tat , Gao, Wei
  • Date: 2014
  • Type: Text , Journal article
  • Relation: International Journal of Solids and Structures Vol. 51, no. 11-12 (June 2014), p. 2096-2108
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  • Description: The dynamic stress and electric displacement intensity factors of impermeable cracks in homogeneous piezoelectric materials and interface cracks in piezoelectric bimaterials are evaluated by extending the scaled boundary finite element method (SBFEM). In this method, a piezoelectric plate is divided into polygons. Each polygon is treated as a scaled boundary finite element subdomain. Only the boundaries of the subdomains need to be discretized with line elements. The dynamic properties of a subdomain are represented by the high order stiffness and mass matrices obtained from a continued fraction solution, which is able to represent the high frequency response with only 3-4 terms per wavelength. The semi-analytical solutions model singular stress and electric displacement fields in the vicinity of crack tips accurately and efficiently. The dynamic stress and electric displacement intensity factors are evaluated directly from the scaled boundary finite element solutions. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required. Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique.

Finite fracture mechanics analysis using the scaled boundary finite element method

- Sun, Zhicheng, Ooi, Ean Tat, Song, Chongmin

  • Authors: Sun, Zhicheng , Ooi, Ean Tat , Song, Chongmin
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Engineering Fracture Mechanics Vol. 134, no. (2015), p. 330-353
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  • Description: The polygon-based scaled boundary finite element method is applied to two finite fracture mechanics based failure criteria to predict the crack initiation from stress concentrations, i.e. notches and holes. The stress and displacement fields are modelled by the scaled boundary finite element method through semi-analytical expressions that resemble asymptotic expansions around cracks and notches. Important fracture parameters, i.e. energy release rate and stress, are accurately and conveniently computed from the solutions of stresses and displacements via analytical integration. One distinguished advantage of applying the scaled boundary finite element method to finite fracture mechanics is that the required changes in the mesh are easily accommodated by shifting the crack tip within the cracked polygon without changing the global mesh structure. The developed framework is validated using four numerical examples. The crack initiation predictions obtained from the scaled boundary finite element method agree well with the reference finite element results.

Crack propagation modelling in functionally graded materials using scaled boundary polygons

- Ooi, Ean Tat, Natarajan, Sundararajan, Song, Chongmin, Tin-Loi, Francis

  • 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.

Modelling multiple cohesive crack propagation using a finite element-scaled boundary finite element coupled method

- Ooi, Ean Tat, Yang, Zhenjun

  • Authors: Ooi, Ean Tat , Yang, Zhenjun
  • Date: 2009
  • Type: Text , Journal article
  • Relation: Engineering Analysis with Boundary Elements Vol. 33, no. 7 (2009), p. 915-929
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  • Description: This paper presents an extension of the recently-developed finite element-scaled boundary finite element (FEM-SBFEM) coupled method to model multiple crack propagation in concrete. The concrete bulk and fracture process zones are modelled using SBFEM and nonlinear cohesive interface finite elements (CIEs), respectively. The CIEs are automatically inserted into the SBFEM mesh as the cracks propagate. The algorithm previously devised for single crack propagation is augmented to model problems with multiple cracks and to allow cracks to initiate in an un-cracked SBFEM mesh. It also addresses crack propagation from one subdomain into another, as a result of partitioning a coarse SBFEM mesh, required for some mixed-mode problems. Each crack in the SBFEM mesh propagates when the sign of the Mode-I stress intensity factor at the crack tip turns positive from negative. Its propagation angle is determined using linear elastic fracture mechanics criteria. Three concrete beams involving multiple crack propagation are modelled. The predicted crack propagation patterns and load-displacement curves are in good agreement with data reported in literature. © 2009 Elsevier Ltd. All rights reserved.

Scaled boundary polygons with application to fracture analysis of functionally graded materials

- Chiong, Irene, Ooi, Ean Tat, Song, Chongmin, Tin-Loi, Francis

Automatic dynamic crack propagation modeling using polygon scaled boundary finite elements

- Ooi, Ean Tat, Shi, Mingguang, Song, Chongmin, Tin-Loi, Francis, Yang, Zhenjun

  • Authors: Ooi, Ean Tat , Shi, Mingguang , Song, Chongmin , Tin-Loi, Francis , Yang, Zhenjun
  • 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 p. 411-416
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  • Description: This study develops a simple and efficient methodology for automatic dynamic crack propagation modeling in structures. It uses high order, arbitrary n-sided polygon elements that are constructed within the scaled boundary finite element framework. Each polygon is treated as a scaled boundary finite element subdomain and their governing equations of equilibrium are assembled using standard finite element procedures. Polygon meshes are automatically generated from a Delaunay triangulated mesh. This method inherits all the positive characteristics of the scaled boundary finite element method. Orders of singularities of any kind can be accurately represented in a unified manner by generalized stress intensity factors to evaluate the crack propagation criterion without dense meshes around the crack tip, special purpose elements or nodal enrichment functions. Crack propagation is efficiently modeled using a simple, yet flexible automatic local remeshing algorithm that is linked to the pre-processing module of a commercial finite element package and can be applied to any polygon mesh. Remeshing involves only polygons around the crack and only minimally changes the global mesh structure. Application of the methodology to model dynamic crack propagation problems is demonstrated by two numerical examples. It is found that the predicted dynamic fracture parameters e.g. dynamic stress intensity factor histories, crack velocity histories, crack length histories and crack paths show good agreement with experiment observations and numerical simulations reported in the literature. © 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

An h-hierarchical adaptive scaled boundary finite element method for elastodynamics

- Yang, Zhenjun, Zhang, Zihua, Liu, Guohua, Ooi, Ean Tat

  • Authors: Yang, Zhenjun , Zhang, Zihua , Liu, Guohua , Ooi, Ean Tat
  • Date: 2011
  • Type: Text , Journal article
  • Relation: Computers and Structures Vol. 89, no. 13-14 (2011), p. 1417-1429
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  • Description: A posteriori h-hierarchical adaptive scaled boundary finite element method (ASBFEM) for transient elastodynamic problems is developed. In a time step, the fields of displacement, stress, velocity and acceleration are all semi-analytical and the kinetic energy, strain energy and energy error are all semi-analytically integrated in subdomains. This makes mesh mapping very simple but accurate. Adaptive mesh refinement is also very simple because only subdomain boundaries are discretised. Two 2D examples with stress wave propagation were modelled. It is found that the degrees of freedom needed by the ASBFEM are only 5%-15% as needed by adaptive FEM for the examples. © 2011 Elsevier Ltd. All rights reserved.

Comparison between single- and dual-porosity models for fluid transport in predicting lesion volume following saline-infused radiofrequency ablation

- Ooi, Ean Hin, Chia, Nicholas, Ooi, Ean Tat, Foo, Ji, Liao, Imam, Nair, Shalini, Mohd Ali, Ahmad

  • 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
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  • 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.

Investigating performance of stormwater filters under controlled and uncontrolled environments

- Meade, Ben, Heyne, Marcus, Li, Lianggang, Jackson, Daniel, Ooi, Ean Tat, Lee, Lisa, Costa, Susanga, Kandra, Harpreet

  • 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
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  • 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.

A novel error indicator and an adaptive refinement technique using the scaled boundary finite element method

- Song, Chongmin, Ooi, Ean Tat, Pramod, Aladurthi, Natarajan, Sundararajan

  • 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
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  • 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 scaled boundary finite element formulation over arbitrary faceted star convex polyhedra

- Natarajan, Sundararajan, Ooi, Ean Tat, Saputra, Albert, Song, Chongmin

  • 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
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  • 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

Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon-quadtree meshes

- Ooi, Ean Tat, Natarajan, Sundararajan, Song, Chongmin, Ooi, Ean Hin

  • 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
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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.

Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method

- Hirshikesh, Pramod, Aladurthi, Annabattula, Ratna, Ooi, Ean Tat, Song, Chongmin, Natarajan, Sundararajan

  • 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
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  • 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.