Numerical recipes for elastodynamic virtual element methods with explicit time integration

Kyoungsoo Park, Heng Chi, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


We present a general framework to solve elastodynamic problems by means of the virtual element method (VEM) with explicit time integration. In particular, the VEM is extended to analyze nearly incompressible solids using the B-bar method. We show that, to establish a B-bar formulation in the VEM setting, one simply needs to modify the stability term to stabilize only the deviatoric part of the stiffness matrix, which requires no additional computational effort. Convergence of the numerical solution is addressed in relation to stability, mass lumping scheme, element size, and distortion of arbitrary elements, either convex or nonconvex. For the estimation of the critical time step, two approaches are presented, ie, the maximum eigenvalue of a system of mass and stiffness matrices and an effective element length. Computational results demonstrate that small edges on convex polygonal elements do not significantly affect the critical time step, whereas convergence of the VEM solution is observed regardless of the stability term and the element shape in both two and three dimensions. This extensive investigation provides numerical recipes for elastodynamic VEMs with explicit time integration and related problems.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalInternational Journal for Numerical Methods in Engineering
Issue number1
StatePublished - Jan 15 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


  • convex and nonconvex elements
  • critical time step
  • elastodynamics
  • lumped mass matrix
  • virtual element method (VEM)


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