Highly accurate solutions and Padé approximants of the stress intensity factors and T-stress for standard specimens

Chowdhury, Morsaleen Shehzad; Song, Chongmin; Gao, Wei

doi:10.1016/j.engfracmech.2015.06.035

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…For the case of the tension test, the domain is approximated via use of a single subdomain with hp-refinement on the boundary to produce gSIFs of highest possible accuracy. Results obtained by this variant are termed SBFEM hi-fi, acknowledging the high fidelity solutions they produce [276].…”

Section: Implemented Variantsmentioning

confidence: 99%

“…The crack paths, however, coalign as expected, although for the PF-FEM the resulting displacements are over-estimated as the fracture must initiate at the same critical load for a given value of G c . An alternate approach, which is highly effective in determining accurate gSIFs [276], may be applied when the domain is star convex with regards to the crack tip, and is introduced here as a high fidelity reference solution (SBFEM hi-fi). Although by hp-refinement on the boundary, the gSIFs are accurately determined utilizing only a few DOFs, and thus minimal computational resources, this approach is only applicable to crack propagation in a select few cases, such as in this symmetric tension test, where the crack path remains straight.…”

Section: Numerical Example 1: Single Edge-notched Tension Testmentioning

confidence: 99%

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Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

et al. 2019

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Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics (LEFM). The purpose of the study is to provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.

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Section: Implemented Variantsmentioning

confidence: 99%

Section: Numerical Example 1: Single Edge-notched Tension Testmentioning

confidence: 99%

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

et al. 2019

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“…The SBFEM was first introduced by Song and Wolf to model unbounded media and was later developed to solve problems for both unbounded and bounded media (see, for example, the works of Wolf and Song and Deeks and Wolf). Using semianalytical solution inside the elements, in bounded media, SBFEM exhibits superior accuracy compared to the FEM, especially for problems involving singularities (see, eg, the works of Chidgzey and Deeks and Chowdhury et al). Among others, SBFEM has been successfully applied to crack analysis and propagation, electromagnetic field problems, elastoplasticity, functionally graded, and composite materials .…”

Section: Introductionmentioning

confidence: 99%

The scaled boundary finite element method for computational homogenization of heterogeneous media

Talebi

Silani

Klusemann

2019

Numerical Meth Engineering

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Materials exhibit macroscopic properties that are dependent on the underlying components at lower scales. Computational homogenization using the finite element method (FEM) is often used to determine the effective mechanical properties based on the microstructure. However, the use of FEM might suffer from several difficulties such as mesh generation, application of periodic boundary conditions or computations in presence of material interfaces, and further discontinuities. In this paper, we present an alternative approach for computational homogenization of heterogeneous structures based on the scaled boundary finite element method (SBFEM). Based on quadtrees, we are applying a simple meshing strategy to create polygonal elements for arbitrary complex microstructures by using a relatively small number of elements. We show on selected numerical examples that the proposed computational homogenization technique represents a suitable alternative to classical FEM approaches capable of avoiding some of the mentioned difficulties while accurately and effectively calculating the macroscopic mechanical properties. An example of a two-scale semiconcurrent coupling between FEM and SBFEM is presented, illustrating the complementarity of both approaches. KEYWORDScomputational homogenization, effective properties, microstructure, polygonal elements, SBFEM Int J Numer Methods Eng. 2019;118:1-17. wileyonlinelibrary.com/journal/nme How to cite this article: Talebi H, Silani M, Klusemann B. The scaled boundary finite element method for computational homogenization of heterogeneous media. Int J Numer Methods Eng. 2019;118:1-17.

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“…The performance of such two methods when applied to three-dimensional crack problems was investigated by Henry and Luxmoore(1995). Recently, a group of techniques based upon scaled boundary finite element methods which combine both analytical feature and the finite element approximation was proposed for the analysis of T-stress of cracks in two-dimensional elastic media (e.g.,Saputra et al, 2015;Chowdhury et al, 2015). While such numerical procedures reduce one spatial dimension in the discretization and provide a direct mean to calculate the fracture data at the crack tip, their computational efficiency is still questionable when dealing with non-planar and multiple cracks and large scale problems.Alternative numerical techniques based upon boundary integral equations have been extensively established for solving linear boundary value problems in mechanics (e.g., Liggett and Liu, 1983; Cruse, 1988; Brebbia and Dominguez, 1989) and they have been proved computationally efficient for linear fracture analysis (e.g., Gu and Yew, 1988; Xu and Ortiz, 1993; Li et al, 1998; Pan and Yuan, 2000; Xu, 2000; Frangi et al, 2002; Ariza and Dominguez, 2004; Rungamornrat and Mear, 2008b,c; Phongtinnabootet al, 2011; Rungamornrat et al, 2015).…”

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confidence: 99%

Weakly singular boundary integral equation method for analysis of generalized T-stresses of cracks in 3D coupled-field media

Sukulthanasorn

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This thesis presents the development of a weakly singular boundary integral equation method for the analysis of the generalized T-stress of isolated cracks embedded in a coupled-field whole space. A pair of weak-form integral equations, one for crack-face generalized traction and the other for the gradient of the crack-face generalized displacement, is established in a general framework allowing various types of materials including elastic, piezoelectric, piezomagnetic and piezoelectromagnetic solids, general crack geometry and loading conditions to be handled in a unified fashion. In addition, the final governing integral equations contain only weakly singular kernels and this, as a result, renders the integral interpretation in terms of Riemann sum and the use of continuous basis functions in the approximation possible. Both symmetric Galerkin boundary element method and the Galerkin technique are employed to solve the pair of weak-form integral equations. Special near-front approximation is also employed to enhance the quality of solution near the crack front with the use of relatively coarse meshes. Explicit formula in terms of the gradient of the sum of the crack-face generalized displacement along the crack front is proposed to extract the generalized T-stress. Extensive results are reported not only to validate the present technique but also to demonstrate its capability and computational robustness

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Highly accurate solutions and Padé approximants of the stress intensity factors and T-stress for standard specimens

Cited by 9 publications

References 10 publications

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

The scaled boundary finite element method for computational homogenization of heterogeneous media

Weakly singular boundary integral equation method for analysis of generalized T-stresses of cracks in 3D coupled-field media

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