Quasi-static crack propagation simulation by an enhanced nodal gradient finite element with different enrichments

Kang, Zuoyi; Bui, Tinh Quoc; Saitoh, Tohru; Hirose, Sohichi

doi:10.1016/j.tafmec.2016.10.006

Cited by 38 publications

(4 citation statements)

References 41 publications

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“…in which [] i l N is the shape function with respect to node i, and n s is the total number of the supporting nodes in regard to the point x. According to [12] and [13], the formulation of the average derivative of the shape functions at node i is given as the following expression (4) in which Δ e is area of the element e.…”

Section: The Consecutive-interpolation 4-node Quadrilateral Element (...mentioning

confidence: 99%

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

Hoang,

Lo,

Tran

et al. 2023

Vietnam J. Sci. Technol.

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This paper investigates fracture mechanics in particle-reinforced composites by using the extended finite element method enhanced by the consecutive-interpolation quadrilateral element. These composite materials have discontinuous boundaries such as cracks, voids, holes, and soft inclusions. And the extended consecutive-interpolation quadrilateral element (XCQ4) is employed to model these boundaries in two-dimensional linear elastic deformation problems. XCQ4 combines the enrichment functions in the traditional extended finite element method with the consecutive interpolation on a 4-node quadrilateral element. This element uses both nodal values and averaged nodal gradients as interpolated conditions. In fracture analysis, the stress intensity factors (SIFs) are important parameters that must be defined. In this study, the values of SIFs at the crack tips are evaluated with the help of the interaction integrals approach. The obtained numerical results are compared with other reliable results showing high accuracy and convergence rate of the XCQ4 element.

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Section: The Consecutive-interpolation 4-node Quadrilateral Element (...mentioning

confidence: 99%

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

Hoang,

Lo,

Tran

et al. 2023

Vietnam J. Sci. Technol.

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“…Generalized quadratures suited for elements with discontinuities were also proposed (Mousavi and Sukumar, 2010a; Mousavi and Sukumar, 2010b). Another option is to subdivide each polygonal sub-domain into triangular cells where the Gauss quadrature can be applied precisely (Moës et al , 1999; Sukumar et al , 2000; Kang et al , 2015; Kang et al , 2017; Chen et al , 2018; Nguyen et al , 2019; Zhou and Chen, 2019). Both strategies conduce to similar results, although the former is limited to two-dimensional spaces.…”

Section: Introductionmentioning

confidence: 99%

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

Campos

Barros

Penna

2020

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Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered. Design/methodology/approach Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results. Findings Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities. Originality/value This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

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“…The SFEM is aimed at improving the performance of conventional finite elements, viz., triangles, quadrilaterals, tetrahedra, hexahedra and in general, arbitrary polytopes. Since its inception, the different variants of the SFEM (such as the edge based SFEM, node based SFEM, cell based SFEM), have been applied to wide variety of problems, such as to fracture mechanics [16][17][18][19][20], incompressible elasticity [21,22], visco-elastoplastic analysis [23][24][25] and impact problems [26], amongst others. The cell based and the edge based SFEM were combined with the XFEM in [17,[27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Adaptive smoothed stable extended finite element method for weak discontinuities for finite elasticity

Jansari

Natarajan

Beex

et al. 2019

European Journal of Mechanics - A/Solids

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Quasi-static crack propagation simulation by an enhanced nodal gradient finite element with different enrichments

Cited by 38 publications

References 41 publications

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

Adaptive smoothed stable extended finite element method for weak discontinuities for finite elasticity

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