A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics

N. Vu-Bac, H. Nguyen-Xuan, L. Chen, C. K. Lee, Goangseup Zi, X. Zhuang, G. R. Liu, Timon Rabczuk

Research output: Contribution to journalArticle

88 Citations (Scopus)

Abstract

This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.

Original languageEnglish
Article number978026
JournalJournal of Applied Mathematics
Volume2013
DOIs
Publication statusPublished - 2013 Aug 19

Fingerprint

Fracture Mechanics
Phantom
Fracture mechanics
Smoothing
Finite element method
Vertex of a graph
Finite Element
Stiffness
Cracks
Extended Finite Element Method
Smoothing Techniques
Shape Function
Numerical Procedure
Modeling Method
Finite Element Model
Simplification
Discontinuity
Crack
High Accuracy
Finite Element Method

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics. / Vu-Bac, N.; Nguyen-Xuan, H.; Chen, L.; Lee, C. K.; Zi, Goangseup; Zhuang, X.; Liu, G. R.; Rabczuk, Timon.

In: Journal of Applied Mathematics, Vol. 2013, 978026, 19.08.2013.

Research output: Contribution to journalArticle

Vu-Bac, N. ; Nguyen-Xuan, H. ; Chen, L. ; Lee, C. K. ; Zi, Goangseup ; Zhuang, X. ; Liu, G. R. ; Rabczuk, Timon. / A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics. In: Journal of Applied Mathematics. 2013 ; Vol. 2013.
@article{af131db27255413887b3b84b291a2f63,
title = "A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics",
abstract = "This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.",
author = "N. Vu-Bac and H. Nguyen-Xuan and L. Chen and Lee, {C. K.} and Goangseup Zi and X. Zhuang and Liu, {G. R.} and Timon Rabczuk",
year = "2013",
month = "8",
day = "19",
doi = "10.1155/2013/978026",
language = "English",
volume = "2013",
journal = "Journal of Applied Mathematics",
issn = "1110-757X",
publisher = "Hindawi Publishing Corporation",

}

TY - JOUR

T1 - A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics

AU - Vu-Bac, N.

AU - Nguyen-Xuan, H.

AU - Chen, L.

AU - Lee, C. K.

AU - Zi, Goangseup

AU - Zhuang, X.

AU - Liu, G. R.

AU - Rabczuk, Timon

PY - 2013/8/19

Y1 - 2013/8/19

N2 - This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.

AB - This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.

UR - http://www.scopus.com/inward/record.url?scp=84881396117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881396117&partnerID=8YFLogxK

U2 - 10.1155/2013/978026

DO - 10.1155/2013/978026

M3 - Article

AN - SCOPUS:84881396117

VL - 2013

JO - Journal of Applied Mathematics

JF - Journal of Applied Mathematics

SN - 1110-757X

M1 - 978026

ER -