On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration

Kyoungsoo Park, Heng Chi, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


While the literature on numerical methods (e.g. finite elements and, to a certain extent, virtual elements) concentrates on convex elements, there is a need to probe beyond this limiting constraint so that the field can be further explored and developed. Thus, in this paper, we employ the virtual element method for non-convex discretizations of elastodynamic problems in 2D and 3D using an explicit time integration scheme. In the formulation, a diagonal matrix-based stabilization scheme is proposed to improve performance and accuracy. To address efficiency, a critical time step is approximated and verified using the maximum eigenvalue of the local (rather than global) system. The computational results demonstrate that the virtual element method is able to consistently handle general nonconvex elements and even non-simply connected elements, which can lead to convenient modeling of arbitrarily-shaped inclusions in composites.

Original languageEnglish (US)
Pages (from-to)669-684
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Nov 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Elastodynamics
  • Non-simply connected elements
  • Nonconvex elements
  • Stabilization
  • Virtual element method (VEM)


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