Details
| Original language | English |
|---|---|
| Pages (from-to) | 366-395 |
| Number of pages | 30 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 340 |
| Early online date | 15 Jun 2018 |
| Publication status | Published - 1 Dec 2018 |
Abstract
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an adaptive mesh refinement strategy based on the superconvergent patch recovery for triangular, quadrilateral as well as for arbitrary polygonal meshes. For the local stiffness matrix in VEM, we adopt a stabilization term which is stable for both isotropic scaling and ratio. Stress intensity factors (SIFs) of a polygonal mesh are discussed and solved by using the interaction domain integral. The present VEM formulations are finally tested and validated by studying its convergence rate for both continuous and discontinuous problems, and are compared with the optimal convergence rate in the conventional Finite Element Method (FEM). Furthermore, the adaptive mesh refinement strategies used to effectively predict the crack growth with the existence of hanging nodes in nonconforming elements are examined.
Keywords
- Adaptive mesh refinement, Crack propagation, Polygonal discretization, Polygonal elements, Virtual Element Method (VEM)
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 340, 01.12.2018, p. 366-395.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A Virtual Element Method for 2D linear elastic fracture analysis
AU - Nguyen-Thanh, Vien Minh
AU - Zhuang, Xiaoying
AU - Nguyen-Xuan, Hung
AU - Rabczuk, Timon
AU - Wriggers, Peter
PY - 2018/12/1
Y1 - 2018/12/1
N2 - This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an adaptive mesh refinement strategy based on the superconvergent patch recovery for triangular, quadrilateral as well as for arbitrary polygonal meshes. For the local stiffness matrix in VEM, we adopt a stabilization term which is stable for both isotropic scaling and ratio. Stress intensity factors (SIFs) of a polygonal mesh are discussed and solved by using the interaction domain integral. The present VEM formulations are finally tested and validated by studying its convergence rate for both continuous and discontinuous problems, and are compared with the optimal convergence rate in the conventional Finite Element Method (FEM). Furthermore, the adaptive mesh refinement strategies used to effectively predict the crack growth with the existence of hanging nodes in nonconforming elements are examined.
AB - This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an adaptive mesh refinement strategy based on the superconvergent patch recovery for triangular, quadrilateral as well as for arbitrary polygonal meshes. For the local stiffness matrix in VEM, we adopt a stabilization term which is stable for both isotropic scaling and ratio. Stress intensity factors (SIFs) of a polygonal mesh are discussed and solved by using the interaction domain integral. The present VEM formulations are finally tested and validated by studying its convergence rate for both continuous and discontinuous problems, and are compared with the optimal convergence rate in the conventional Finite Element Method (FEM). Furthermore, the adaptive mesh refinement strategies used to effectively predict the crack growth with the existence of hanging nodes in nonconforming elements are examined.
KW - Adaptive mesh refinement
KW - Crack propagation
KW - Polygonal discretization
KW - Polygonal elements
KW - Virtual Element Method (VEM)
UR - http://www.scopus.com/inward/record.url?scp=85050493497&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1808.00355
DO - 10.48550/arXiv.1808.00355
M3 - Article
AN - SCOPUS:85050493497
VL - 340
SP - 366
EP - 395
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -