Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description

Thomas Peter Fries, Malak Baydoun

Research output: Contribution to journalArticleResearchpeer-review

Abstract

A method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward.

Original languageEnglish
Pages (from-to)1527-1558
Number of pages32
JournalInternational journal for numerical methods in engineering
Volume89
Issue number12
DOIs
Publication statusPublished - 23 Mar 2012

Fingerprint

Extended Finite Element Method
Crack Propagation
Crack propagation
Crack
Cracks
Finite element method
Three-dimensional
Simulation
Remeshing
Level Set Method
Fracture Mechanics
Fracture mechanics
Level Set
Polyhedron
Three-dimension
Update
Propagation
Imply

Keywords

  • Crack propagation
  • Extended finite element method (XFEM)
  • GFEM

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description. / Fries, Thomas Peter; Baydoun, Malak.

In: International journal for numerical methods in engineering, Vol. 89, No. 12, 23.03.2012, p. 1527-1558.

Research output: Contribution to journalArticleResearchpeer-review

@article{b3e55ca1e5004260bf017245b3755697,
title = "Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description",
abstract = "A method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward.",
keywords = "Crack propagation, Extended finite element method (XFEM), GFEM",
author = "Fries, {Thomas Peter} and Malak Baydoun",
year = "2012",
month = "3",
day = "23",
doi = "10.1002/nme.3299",
language = "English",
volume = "89",
pages = "1527--1558",
journal = "International journal for numerical methods in engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "12",

}

TY - JOUR

T1 - Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description

AU - Fries, Thomas Peter

AU - Baydoun, Malak

PY - 2012/3/23

Y1 - 2012/3/23

N2 - A method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward.

AB - A method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward.

KW - Crack propagation

KW - Extended finite element method (XFEM)

KW - GFEM

UR - http://www.scopus.com/inward/record.url?scp=84857357512&partnerID=8YFLogxK

U2 - 10.1002/nme.3299

DO - 10.1002/nme.3299

M3 - Article

VL - 89

SP - 1527

EP - 1558

JO - International journal for numerical methods in engineering

JF - International journal for numerical methods in engineering

SN - 0029-5981

IS - 12

ER -