The perturbation method and the extended finite element method. An application to fracture mechanics problems

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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Stability and convergence proofs for a discontinuous-Galerkin-based extended finite element method for fracture mechanics

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2010.03.008 ◽

2010 ◽

Vol 199 (37-40) ◽

pp. 2360-2382 ◽

Cited By ~ 9

Author(s):

Yongxing Shen ◽

Adrian Lew

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Fracture Mechanics ◽

Discontinuous Galerkin ◽

Extended Finite Element Method ◽

Stability And Convergence ◽

Extended Finite Element ◽

Convergence Proofs ◽

Element Method

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Extended Finite Element Method for Fracture Mechanics and Mesh Refinement Controlled by Density Function

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.525-526.413 ◽

2012 ◽

Vol 525-526 ◽

pp. 413-416

Author(s):

Yi Cen

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Fracture Mechanics ◽

Numerical Method ◽

Density Function ◽

Extended Finite Element Method ◽

Mesh Refinement ◽

Extended Finite Element ◽

Element Enrichment ◽

Element Method

This paper discusses the combination of element enrichment by mesh refinement controlled by density function with the extended finite element method and its application in fracture mechanics. Extended finite element method (XFEM) is an effective numerical method for solving discontinuity problems in the finite element work frame. A numerical example of fracture mechanics is analyzed at the end of this paper to show the application of the above method.

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Cast3M implementation of the extended finite element method for cohesive crack

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/33/1/38 ◽

2011 ◽

Vol 33 (1) ◽

pp. 55-64

Author(s):

Nguyen Truong Giang ◽

Ngo Huong Nhu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Fracture Mechanics ◽

Extended Finite Element Method ◽

Brittle Materials ◽

Cohesive Crack ◽

Numerical Calculations ◽

Extended Finite Element ◽

Element Method

In this paper, the finite element for cohesive crack for quasi-brittle materials is constructed by the displacement discontinuities in the element. The algorithm of construction and procedures for involving this finite element into code Cast3M are presented. The numerical calculations in fracture mechanics are presented to demonstrate the benefits of the proposed implementation.

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