Some Improvements for Extended Finite Element Methods in Fracture Mechanics

2008 ◽  
pp. 953-954
Author(s):  
Patrick Laborde ◽  
Julien Pommier ◽  
Yves Renard ◽  
Michel Salaun
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Finite Element Methods ◽  
Extended Finite Element

A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics

2019 ◽  
Vol 230 (7) ◽  
pp. 2385-2398 ◽  
Author(s):  
S. Z. Feng ◽  
S. P. A. Bordas ◽  
X. Han ◽  
G. Wang ◽  
Z. X. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Element Method

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

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bruna Caroline Campos ◽  
Felício Bruzzi Barros ◽  
Samuel Silva Penna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Content Type ◽  
Integration Techniques ◽  
Integration Strategies ◽  
Element Method

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.

scholarly journals Structured extended finite element methods for solids defined by implicit surfaces

2002 ◽  
Vol 56 (4) ◽  
pp. 609-635 ◽  
Author(s):  
Ted Belytschko ◽  
Chandu Parimi ◽  
Nicolas Moës ◽  
N. Sukumar ◽  
Shuji Usui
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Implicit Surfaces ◽  
Extended Finite Element
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