Abstract
SUMMARY: This paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra-elemental discontinuities in 2D solids. The augmented finite element method (A-FEM) employs four internal nodes to account for the crack displacements due to an intra-elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece-wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A-FEM's high-fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A-FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust.
| Original language | English |
|---|---|
| Pages (from-to) | 438-468 |
| Number of pages | 31 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 99 |
| Issue number | 6 |
| DOIs | |
| State | Published - Aug 10 2014 |
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Keywords
- Composites
- Damage
- Finite element methods
- Fracture
- Stability
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
- Numerical Analysis
Cite this
An efficient augmented finite element method for arbitrary cracking and crack interaction in solids. / Liu, W.; Yang, Qingda; Mohammadizadeh, S.; Su, X. Y.
In: International Journal for Numerical Methods in Engineering, Vol. 99, No. 6, 10.08.2014, p. 438-468.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An efficient augmented finite element method for arbitrary cracking and crack interaction in solids
AU - Liu, W.
AU - Yang, Qingda
AU - Mohammadizadeh, S.
AU - Su, X. Y.
PY - 2014/8/10
Y1 - 2014/8/10
N2 - SUMMARY: This paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra-elemental discontinuities in 2D solids. The augmented finite element method (A-FEM) employs four internal nodes to account for the crack displacements due to an intra-elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece-wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A-FEM's high-fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A-FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust.
AB - SUMMARY: This paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra-elemental discontinuities in 2D solids. The augmented finite element method (A-FEM) employs four internal nodes to account for the crack displacements due to an intra-elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece-wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A-FEM's high-fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A-FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust.
KW - Composites
KW - Damage
KW - Finite element methods
KW - Fracture
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84903997255&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903997255&partnerID=8YFLogxK
U2 - 10.1002/nme.4697
DO - 10.1002/nme.4697
M3 - Article
AN - SCOPUS:84903997255
VL - 99
SP - 438
EP - 468
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 6
ER -