New anisotropic crack-tip enrichment functions for the extended finite element method

Hattori, Gabriel; Rojas-Díaz, R.; Sáez, Andrés; Sukumar, N.; García-Sánchez, F.

doi:10.1007/s00466-012-0691-0

Cited by 41 publications

(31 citation statements)

References 24 publications

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“…In this example, the Poisson's ratio and the shear modulus are taken as: ν 12 = 0.03, and G 12 = 6 GPa, respectively. The Young's moduli E 1 and E 2 are computed from the following expressions :

\begin{matrix} left \\ E_{1} = G_{12} (Φ + 2 υ_{12} + 1) \\ E_{2} = \frac{E_{1}}{Φ} \end{matrix}

where Φ is the material parameter defined by the ratio between the Young's moduli. Figure shows the influence of the material parameter on the normalized mode I SIF

MathClass-open(K_{I} MathClass-bin∕ MathClass-open(σ \sqrt{πa} MathClass-close) MathClass-close)

.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Figure shows the influence of the material parameter on the normalized mode I SIF

MathClass-open(K_{I} MathClass-bin∕ MathClass-open(σ \sqrt{πa} MathClass-close) MathClass-close)

. The results are compared with those obtained in Reference . It is emphasized that in Reference , new set of enrichment functions are derived for anisotropic materials, and as such, no enrichment functions are required in the proposed technique.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…p a//. The results are compared with those obtained in Reference [64]. It is emphasized that in Reference [64], new set of enrichment functions are derived for anisotropic materials, and as such, no enrichment functions are required in the proposed technique.…”

Section: Rectangular Plate With An Inclined Crack In Tensionmentioning

confidence: 99%

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Representation of singular fields without asymptotic enrichment in the extended finite element method

Natarajan

Song

2013

Numerical Meth Engineering

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SUMMARYIn this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi‐analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does not require special numerical integration technique to compute the stiffness matrix, and it improves the capability of the XFEM to model cracks in homogeneous and/or heterogeneous materials without a priori knowledge of the asymptotic solutions. A Heaviside enrichment is used to represent the jump across the discontinuity surface. We call the method as the extended SBFEM. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics show that the proposed method yields accurate results with improved condition number. A simple code is annexed to compute the terms in the stiffness matrix, which can easily be integrated in any existing FEM/XFEM code. Copyright © 2013 John Wiley & Sons, Ltd.

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\begin{matrix} left \\ E_{1} = G_{12} (Φ + 2 υ_{12} + 1) \\ E_{2} = \frac{E_{1}}{Φ} \end{matrix}

where Φ is the material parameter defined by the ratio between the Young's moduli. Figure shows the influence of the material parameter on the normalized mode I SIF

MathClass-open(K_{I} MathClass-bin∕ MathClass-open(σ \sqrt{πa} MathClass-close) MathClass-close)

.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Figure shows the influence of the material parameter on the normalized mode I SIF

MathClass-open(K_{I} MathClass-bin∕ MathClass-open(σ \sqrt{πa} MathClass-close) MathClass-close)

Section: Numerical Examplesmentioning

confidence: 99%

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Representation of singular fields without asymptotic enrichment in the extended finite element method

Natarajan

Song

2013

Numerical Meth Engineering

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“…Namely among them are Belytschko et al (2003), Sukumar and Prevost (2003), Bellec and Dolbow (2003), Sukumar et al (2005), Belytschko et al (2005), Asadpoure et al (2006a, b), Sladek et al (2006), Asadpoure and Mohammadi (2007), Belytschko and Gracie (2007), Tabarraei and Sukumar (2008), Giner et al (2009), Abdelaziz and Hamouine (2008), Ebrahimi et al (2008), Shibanuma and Utsunomiya (2009), Richardson et al (2009), Liang et al (2010), Hattori et al (2012), Mousavi and Sukumar (2010), Ghorashi et al (2011) and Chatzi et al (2011).…”

Section: Introductionmentioning

confidence: 97%

Stochastic fracture analysis of laminated composite plate with arbitrary cracks using X-FEM

Lal

Palekar

2015

Int J Mech Mater Des

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In this paper, second order statistics of mixed mode stress intensity factors (MSIFs) and crack propagation analysis of the symmetric angle ply laminated composite plate with through thickness arbitrary curve cracks subjected to tensile and shear stress is presented. The fracture behaviour is analysed using extended finite element method (X-FEM). The cracks like line, semi elliptical, semi circular and arbitrary curves are considered for the detailed numerical study. The material properties, lamination angle, loading, crack width and crack depth are modelled as independent, combine uncorrelated and correlated input random Gaussian variables. The interaction integral (M-integral) is adopted for calculating the MSIFs. The second order perturbation technique and Monte Carlo simulations are proposed to obtain the mean and coefficient of variance of MSIFs by random change in input system parameters. This work signifies the accurate and realistic evaluation of fracture response by handling the various levels of uncertainties. The effect of crack propagation on MSIFs using tensile and shear stresses using global tracking algorithm is also highlighted.

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“…Modelling cracking using XFEM in Abaqus uses the method developed by Belytschko and Black [19] who proposed local enrichment functions to incorporate the presence of a discontinuity caused by the cracking of a material. In Abaqus, crack propagation depends on the nodal displacements of the elements near the crack tip.…”

Section: Xfem Assumptionsmentioning

confidence: 99%

Crack Propagation for Concrete Flat Plates Using XFEM Method

Al‐Hamd¹,

Gillie²,

Wang

et al. 2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Flat plate concrete structures are easy to construct and cheap to build. However, they are susceptible to a type of brittle failure known as "punching shear", where columns punch through the floor leading to progressive collapse. This is a particularly dangerous type of failure as it occurs suddenly and without warning. A finite element model was developed and validated based on the author's previous tests for a square slab with a single column stub. This arrangement simulates the type of column to slab arrangement found in many office buildings. The failure mechanics were examined and the model gave a good agreement with the experimental results identifying the correct crack pattern and the failure loads. A 2-d axisymmetric model was then developed representing a circular column to model the punching crack propagation in detail. This was done using the extended finite element method (XFEM). The XFEM results showed the good agreement between crack location and areas of highest principal strain and were able to capture crack propagation and the effect this has on the stress state under punching failure. It is concluded that explicit modelling of fracture is beneficial in order to capture the full response of the slab and that continuum models are insufficient to do this.

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New anisotropic crack-tip enrichment functions for the extended finite element method

Cited by 41 publications

References 24 publications

Representation of singular fields without asymptotic enrichment in the extended finite element method

Representation of singular fields without asymptotic enrichment in the extended finite element method

Stochastic fracture analysis of laminated composite plate with arbitrary cracks using X-FEM

Crack Propagation for Concrete Flat Plates Using XFEM Method

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