A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis

N. Vu-Bac, H. Nguyen-Xuan, L. Chen, S. Bordas, P. Kerfriden, R. N. Simpson, G. R. Liu, Timon Rabczuk

Research output: Contribution to journalArticle

78 Citations (Scopus)

Abstract

This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results.

Original languageEnglish
Pages (from-to)331-355
Number of pages25
JournalCMES - Computer Modeling in Engineering and Sciences
Volume73
Issue number4
Publication statusPublished - 2011 Jul 6
Externally publishedYes

Fingerprint

Extended Finite Element Method
Finite element method
Vertex of a graph
Smoothing
Finite Element Method
Stress Singularity
Smoothing Techniques
Stiffness matrix
Crack Tip
Shape Function
Stress Intensity Factor
Stiffness Matrix
Stress intensity factors
Crack tips
Divides
Elasticity
Numerical methods
Crack
Interior
Numerical Methods

Keywords

  • Convergence rate
  • Extended finite element method
  • Fracture analysis
  • Node-based smoothed finite element method
  • Numerical method
  • Stress intensity factor (SIF)

ASJC Scopus subject areas

  • Computer Science Applications
  • Software
  • Modelling and Simulation

Cite this

Vu-Bac, N., Nguyen-Xuan, H., Chen, L., Bordas, S., Kerfriden, P., Simpson, R. N., ... Rabczuk, T. (2011). A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. CMES - Computer Modeling in Engineering and Sciences, 73(4), 331-355.

A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. / Vu-Bac, N.; Nguyen-Xuan, H.; Chen, L.; Bordas, S.; Kerfriden, P.; Simpson, R. N.; Liu, G. R.; Rabczuk, Timon.

In: CMES - Computer Modeling in Engineering and Sciences, Vol. 73, No. 4, 06.07.2011, p. 331-355.

Research output: Contribution to journalArticle

Vu-Bac, N, Nguyen-Xuan, H, Chen, L, Bordas, S, Kerfriden, P, Simpson, RN, Liu, GR & Rabczuk, T 2011, 'A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis', CMES - Computer Modeling in Engineering and Sciences, vol. 73, no. 4, pp. 331-355.
Vu-Bac N, Nguyen-Xuan H, Chen L, Bordas S, Kerfriden P, Simpson RN et al. A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. CMES - Computer Modeling in Engineering and Sciences. 2011 Jul 6;73(4):331-355.
Vu-Bac, N. ; Nguyen-Xuan, H. ; Chen, L. ; Bordas, S. ; Kerfriden, P. ; Simpson, R. N. ; Liu, G. R. ; Rabczuk, Timon. / A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. In: CMES - Computer Modeling in Engineering and Sciences. 2011 ; Vol. 73, No. 4. pp. 331-355.
@article{3ad943545662470498cfc0019d6c3667,
title = "A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis",
abstract = "This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results.",
keywords = "Convergence rate, Extended finite element method, Fracture analysis, Node-based smoothed finite element method, Numerical method, Stress intensity factor (SIF)",
author = "N. Vu-Bac and H. Nguyen-Xuan and L. Chen and S. Bordas and P. Kerfriden and Simpson, {R. N.} and Liu, {G. R.} and Timon Rabczuk",
year = "2011",
month = "7",
day = "6",
language = "English",
volume = "73",
pages = "331--355",
journal = "CMES - Computer Modeling in Engineering and Sciences",
issn = "1526-1492",
publisher = "Tech Science Press",
number = "4",

}

TY - JOUR

T1 - A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis

AU - Vu-Bac, N.

AU - Nguyen-Xuan, H.

AU - Chen, L.

AU - Bordas, S.

AU - Kerfriden, P.

AU - Simpson, R. N.

AU - Liu, G. R.

AU - Rabczuk, Timon

PY - 2011/7/6

Y1 - 2011/7/6

N2 - This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results.

AB - This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results.

KW - Convergence rate

KW - Extended finite element method

KW - Fracture analysis

KW - Node-based smoothed finite element method

KW - Numerical method

KW - Stress intensity factor (SIF)

UR - http://www.scopus.com/inward/record.url?scp=79959841835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959841835&partnerID=8YFLogxK

M3 - Article

VL - 73

SP - 331

EP - 355

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 4

ER -