A Virtual Element Method for 2D linear elastic fracture analysis

Vien Minh Nguyen-Thanh, Xiaoying Zhuang, Hung Nguyen-Xuan, Timon Rabczuk, Peter Wriggers

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)366-395
Number of pages30
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2018 Oct 1
Externally publishedYes


  • Adaptive mesh refinement
  • Crack propagation
  • Polygonal discretization
  • Polygonal elements
  • Virtual Element Method (VEM)

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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