Abstract
In this paper a new augmented finite element method (A-FEM) that can account for multiple, intra-elemental discontinuities in heterogeneous solids has been derived. It does not need the extra DoFs as in the extended finite element method (X-FEM), or the additional nodes as in the phantom node method (PNM). The new A-FEM employs four internal nodes to facilitate the calculation of subdomain stiffness and the crack displacements due to an intra-elemental discontinuity. It is shown that through a novel efficient solving algorithm the displacement DoFs associated with the internal nodes can be solved analytically as functions of the regular nodal DoFs for any piece-wise linear cohesive laws, which leads to a fully-condensed elemental equilibrium equation that is mathematically exact. The new formulation permits repeated elemental augmentation to include multiple interactive cracks within a single element, enabling a unified treatment of the evolution from a weak discontinuity, to a strong discontinuity, and to multiple intra-element discontinuities, all within a single element that employs standard DoFs only. The new A-FEM's capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples. It has been demonstrated that the new A-FEM achieved more than two orders of magnitude improvement in numerical accuracy, efficiency, and robustness, compared to the X-FEM.
| Original language | English |
|---|---|
| Title of host publication | 13th International Conference on Fracture 2013, ICF 2013 |
| Publisher | Chinese Society of Theoretical and Applied Mechanics |
| Pages | 3551-3560 |
| Number of pages | 10 |
| Volume | 5 |
| State | Published - Jan 1 2013 |
| Event | 13th International Conference on Fracture 2013, ICF 2013 - Beijing, China Duration: Jun 16 2013 → Jun 21 2013 |
Other
| Other | 13th International Conference on Fracture 2013, ICF 2013 |
|---|---|
| Country | China |
| City | Beijing |
| Period | 6/16/13 → 6/21/13 |
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Keywords
- Augmented FEM
- Cohesive model
- Extended FEM
- Fracture
- Numerical simulation
ASJC Scopus subject areas
- Geotechnical Engineering and Engineering Geology
Cite this
An efficient A-FEM for arbitrary cracking in solids. / Yang, Qingda; Liu, Wei; Su, Xian Yue.
13th International Conference on Fracture 2013, ICF 2013. Vol. 5 Chinese Society of Theoretical and Applied Mechanics, 2013. p. 3551-3560.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - An efficient A-FEM for arbitrary cracking in solids
AU - Yang, Qingda
AU - Liu, Wei
AU - Su, Xian Yue
PY - 2013/1/1
Y1 - 2013/1/1
N2 - In this paper a new augmented finite element method (A-FEM) that can account for multiple, intra-elemental discontinuities in heterogeneous solids has been derived. It does not need the extra DoFs as in the extended finite element method (X-FEM), or the additional nodes as in the phantom node method (PNM). The new A-FEM employs four internal nodes to facilitate the calculation of subdomain stiffness and the crack displacements due to an intra-elemental discontinuity. It is shown that through a novel efficient solving algorithm the displacement DoFs associated with the internal nodes can be solved analytically as functions of the regular nodal DoFs for any piece-wise linear cohesive laws, which leads to a fully-condensed elemental equilibrium equation that is mathematically exact. The new formulation permits repeated elemental augmentation to include multiple interactive cracks within a single element, enabling a unified treatment of the evolution from a weak discontinuity, to a strong discontinuity, and to multiple intra-element discontinuities, all within a single element that employs standard DoFs only. The new A-FEM's capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples. It has been demonstrated that the new A-FEM achieved more than two orders of magnitude improvement in numerical accuracy, efficiency, and robustness, compared to the X-FEM.
AB - In this paper a new augmented finite element method (A-FEM) that can account for multiple, intra-elemental discontinuities in heterogeneous solids has been derived. It does not need the extra DoFs as in the extended finite element method (X-FEM), or the additional nodes as in the phantom node method (PNM). The new A-FEM employs four internal nodes to facilitate the calculation of subdomain stiffness and the crack displacements due to an intra-elemental discontinuity. It is shown that through a novel efficient solving algorithm the displacement DoFs associated with the internal nodes can be solved analytically as functions of the regular nodal DoFs for any piece-wise linear cohesive laws, which leads to a fully-condensed elemental equilibrium equation that is mathematically exact. The new formulation permits repeated elemental augmentation to include multiple interactive cracks within a single element, enabling a unified treatment of the evolution from a weak discontinuity, to a strong discontinuity, and to multiple intra-element discontinuities, all within a single element that employs standard DoFs only. The new A-FEM's capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples. It has been demonstrated that the new A-FEM achieved more than two orders of magnitude improvement in numerical accuracy, efficiency, and robustness, compared to the X-FEM.
KW - Augmented FEM
KW - Cohesive model
KW - Extended FEM
KW - Fracture
KW - Numerical simulation
UR - http://www.scopus.com/inward/record.url?scp=84898787044&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84898787044&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84898787044
VL - 5
SP - 3551
EP - 3560
BT - 13th International Conference on Fracture 2013, ICF 2013
PB - Chinese Society of Theoretical and Applied Mechanics
ER -