An accurate and efficient augmented finite element method for arbitrary crack interactions

W. Liu, Qingda Yang, S. Mohammadizadeh, X. Y. Su, D. S. Ling

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

This paper presents a new augmented finite element method (A-FEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method (X-FEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoFs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-FEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.

Original languageEnglish
Article number041033
JournalJournal of Applied Mechanics, Transactions ASME
Volume80
Issue number4
DOIs
StatePublished - Jan 1 2013

Fingerprint

equilibrium equations
finite element method
cracks
Cracks
Finite element method
traction
interactions
discontinuity
derivation
degrees of freedom
formulations
augmentation
simulation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

An accurate and efficient augmented finite element method for arbitrary crack interactions. / Liu, W.; Yang, Qingda; Mohammadizadeh, S.; Su, X. Y.; Ling, D. S.

In: Journal of Applied Mechanics, Transactions ASME, Vol. 80, No. 4, 041033, 01.01.2013.

Research output: Contribution to journalArticle

@article{07b9562076894961a7346a252846b732,
title = "An accurate and efficient augmented finite element method for arbitrary crack interactions",
abstract = "This paper presents a new augmented finite element method (A-FEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method (X-FEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoFs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-FEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.",
author = "W. Liu and Qingda Yang and S. Mohammadizadeh and Su, {X. Y.} and Ling, {D. S.}",
year = "2013",
month = "1",
day = "1",
doi = "10.1115/1.4007970",
language = "English",
volume = "80",
journal = "Journal of Applied Mechanics, Transactions ASME",
issn = "0021-8936",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "4",

}

TY - JOUR

T1 - An accurate and efficient augmented finite element method for arbitrary crack interactions

AU - Liu, W.

AU - Yang, Qingda

AU - Mohammadizadeh, S.

AU - Su, X. Y.

AU - Ling, D. S.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - This paper presents a new augmented finite element method (A-FEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method (X-FEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoFs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-FEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.

AB - This paper presents a new augmented finite element method (A-FEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method (X-FEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoFs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-FEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=84903593290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903593290&partnerID=8YFLogxK

U2 - 10.1115/1.4007970

DO - 10.1115/1.4007970

M3 - Article

AN - SCOPUS:84903593290

VL - 80

JO - Journal of Applied Mechanics, Transactions ASME

JF - Journal of Applied Mechanics, Transactions ASME

SN - 0021-8936

IS - 4

M1 - 041033

ER -