Orthotropic enriched element free Galerkin method for fracture analysis of composites

Ghorashi, Seyed Shahram; Mohammadi, Soheil; Sabbagh-Yazdi, Saeed-Reza

doi:10.1016/j.engfracmech.2011.03.011

Cited by 82 publications

(32 citation statements)

References 33 publications

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“…In this study, a subtriangles technique originated from XFEM and similar to the one proposed by Ghorashi et al for the element free Galerkin method (EFGM) is employed to overcome the reduction of accuracy of integration. As illustrated in Figure , when employing the subtriangles technique, elements intersected with a crack is subdivided at both sides into subtriangles whose edges are adjusted to the crack faces.…”

Section: Extended Isogeometric Analysismentioning

confidence: 99%

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Extended isogeometric analysis for simulation of stationary and propagating cracks

Ghorashi

Valizadeh

Mohammadi

2011

Numerical Meth Engineering

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224

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SUMMARYA novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B-splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two-dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed-mode stress intensity factors are compared with analytical and extended FEM results.

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Section: Extended Isogeometric Analysismentioning

confidence: 99%

“…The subtriangles technique for partitioning the cracked elements : (a) crack edge and (b) crack tip.…”

Section: Extended Isogeometric Analysismentioning

confidence: 99%

Extended isogeometric analysis for simulation of stationary and propagating cracks

Ghorashi

Valizadeh

Mohammadi

2011

Numerical Meth Engineering

Self Cite

224

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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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“…Four types of finite elements are distinguished in these examples according to their positions with respect to the crack, the standard element contains 3×3 Gauss points. The element having tip enriched control points contains 7×7 Gauss points and the sub-triangle technique (Ghorashi et al, 2011) is used for the tip-element by 13 Gauss points in each triangle, however the split element contains 6×6 Gauss points for the horizontal crack problems and the sub-triangle technique is used by 13 Gauss points in each triangle for the inclined crack problems. The SIFs are evaluated using interaction integral (Yau and Wang, 1984), wherein the crack tip element is not considered in the calculation.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Crack analysis in bimaterial interfaces using T-spline based XIGA

Habib

Belaidi

2017

jtam

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Analysis-suitable T-splines are used for the modeling and analyzing of cracks in bimaterial interfaces within the framework of an extended isogeometric analysis (XIGA). The crack tip enrichment functions of bimaterial interface cracks are implemented to reproduce singular fields, and the signed distance functions are used to treat the crack face and the interface in the models. A compatible local refinement algorithm is applied to refine location of the crack and the interface, which helps one to avoid produce excessive propagation of control points. The mixed mode stress intensity factors (SIFs) which are evaluated by the interaction integral (M-integral) are used as analysis parameters. Numerical simulations are performed to analyze the problem and to examine the efficiency of the proposed method. The obtained results are compared with other available results.

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Orthotropic enriched element free Galerkin method for fracture analysis of composites

Cited by 82 publications

References 33 publications

Extended isogeometric analysis for simulation of stationary and propagating cracks

Extended isogeometric analysis for simulation of stationary and propagating cracks

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

Crack analysis in bimaterial interfaces using T-spline based XIGA

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