minhnguyenikm / vem

Virtual Element Method

vem

Virtual Element Method

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Author: Nguyen Thanh Vien Minh

Email: [email protected] (institute email: [email protected])

Working at: Institut fuer Kontinuumsmechanik, Hannover, Germany

Website: https://www.ikm.uni-hannover.de/kontinuumsmechanik.html?&no_cache=1&L=1

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Please cite the paper if you would like to use my source code as a part of your project

A Virtual Element Method for 2D linear elastic fracture analysis
Vien Minh Nguyen-Thanh, Xiaoying Zhuang, Hung Nguyen-Xuan, Timon Rabczuk, Peter Wriggers,
Computer Methods in Applied Mechanics and Engineering,
Volume 340,
2018,
Pages 366-395,
ISSN 0045-7825,
https://doi.org/10.1016/j.cma.2018.05.021.
(http://www.sciencedirect.com/science/article/pii/S0045782518302664)
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: Virtual Element Method (VEM); Crack propagation; Polygonal discretization; Polygonal elements; Adaptive mesh refinement

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