Some basic formulations of the virtual element method (VEM) for finite deformations

H. Chi, L. Beirão da Veiga, G. H. Paulino

Research output: Contribution to journalArticlepeer-review

141 Scopus citations


We present a general virtual element method (VEM) framework for finite elasticity, which emphasizes two issues: element-level volume change (volume average of the determinant of the deformation gradient) and stabilization. To address the former issue, we provide exact evaluation of the average volume change in both 2D and 3D on properly constructed local displacement spaces. For the later issue, we provide a new stabilization scheme that is based on the trace of the material tangent modulus tensor, which captures highly heterogeneous and localized deformations. Two VEM formulations are presented: a two-field mixed and an equivalent displacement-based, which is free of volumetric locking. Convergence and accuracy of the VEM formulations are verified by means of numerical examples, and engineering applications are demonstrated.

Original languageEnglish (US)
Pages (from-to)148-192
Number of pages45
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - May 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Filled elastomers
  • Finite elasticity
  • Mixed variational principle
  • Virtual element method (VEM)


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