A Virtual Element Method for 2D linear elastic fracture analysis

authored by: Vien Minh Nguyen-Thanh, Xiaoying Zhuang, Hung Nguyen-Xuan, Timon Rabczuk, Peter Wriggers
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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Vietnam National University Ho Chi Minh City
Sejong University
Bauhaus-Universität Weimar
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 340
Pages: 366-395
No. of pages: 30
ISSN: 0045-7825
Publication date: 01.12.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.48550/arXiv.1808.00355 (Access: Open)
https://doi.org/10.1016/j.cma.2018.05.021 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{311c934939524de98bb803b3f300f1e3,
title = "A Virtual Element Method for 2D linear elastic fracture analysis",
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)",
author = "Nguyen-Thanh, {Vien Minh} and Xiaoying Zhuang and Hung Nguyen-Xuan and Timon Rabczuk and Peter Wriggers",
year = "2018",
month = dec,
day = "1",
doi = "10.48550/arXiv.1808.00355",
language = "English",
volume = "340",
pages = "366--395",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}