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

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Bibliographic Details
Published in:Engineering computations Vol. 38; no. 1; pp. 180 - 220
Main Authors: Campos, Bruna Caroline, Barros, Felício Bruzzi, Penna, Samuel Silva
Format: Journal Article
Language:English
Published: Bradford Emerald Publishing Limited 27.01.2021
Emerald Group Publishing Limited
Subjects:
Approximation
Crack propagation
Finite element analysis
Finite element method
Fracture mechanics
Integrals
Linear elastic fracture mechanics
Methods
Numerical integration
Parameters
Propagation
Quadratures
Stress intensity factors
Computational mechanics
Fracture mechanics
Numerical integration
Generalized/extended finite element method
Partition of unity methods
ISSN:0264-4401, 1758-7077
Online Access:Get full text
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Summary: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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ISSN:0264-4401
1758-7077
DOI:10.1108/EC-02-2020-0067