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.
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July 2013
Research-Article
An Accurate and Efficient Augmented Finite Element Method for Arbitrary Crack Interactions
W. Liu,
W. Liu
Department of Mechanical and Aerospace Engineering
,University of Miami
,Coral Gables, FL 33124
;Department of Mechanics and Aerospace Engineering
,Peking University
,Beijing 100871
, China
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Q. D. Yang,
Q. D. Yang
1
Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33124
e-mail: qdyang@miami.edu
University of Miami,
Coral Gables, FL 33124
e-mail: qdyang@miami.edu
1Corresponding author.
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S. Mohammadizadeh,
S. Mohammadizadeh
Department of Mechanical and Aerospace Engineering
,University of Miami
,Coral Gables, FL 33124
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X. Y. Su,
X. Y. Su
Department of Mechanics and Aerospace Engineering
,Peking University
,Beijing 100871
, China
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D. S. Ling
D. S. Ling
Department of Civil Engineering
,Zhejiang University
,Hangzhou 310058
, China
Search for other works by this author on:
W. Liu
Department of Mechanical and Aerospace Engineering
,University of Miami
,Coral Gables, FL 33124
;Department of Mechanics and Aerospace Engineering
,Peking University
,Beijing 100871
, China
Q. D. Yang
Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33124
e-mail: qdyang@miami.edu
University of Miami,
Coral Gables, FL 33124
e-mail: qdyang@miami.edu
S. Mohammadizadeh
Department of Mechanical and Aerospace Engineering
,University of Miami
,Coral Gables, FL 33124
X. Y. Su
Department of Mechanics and Aerospace Engineering
,Peking University
,Beijing 100871
, China
D. S. Ling
Department of Civil Engineering
,Zhejiang University
,Hangzhou 310058
, China
1Corresponding author.
Manuscript received September 9, 2012; final manuscript received October 2, 2012; accepted manuscript posted October 30, 2012; published online May 31, 2013. Editor: Yonggang Huang.
J. Appl. Mech. Jul 2013, 80(4): 041033 (12 pages)
Published Online: May 31, 2013
Article history
Received:
September 9, 2012
Revision Received:
October 2, 2012
Accepted:
October 3, 2012
Citation
Liu, W., Yang, Q. D., Mohammadizadeh, S., Su, X. Y., and Ling, D. S. (May 31, 2013). "An Accurate and Efficient Augmented Finite Element Method for Arbitrary Crack Interactions." ASME. J. Appl. Mech. July 2013; 80(4): 041033. https://doi.org/10.1115/1.4007970
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