B-bar virtual element method for nearly incompressible and compressible materials

Kyoungsoo Park, Heng Chi, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We present a B-bar formulation of the virtual element method (VEM) for the analysis of both nearly incompressible and compressible materials. The material stiffness is decomposed into dilatational and deviatoric parts, and only the deviatoric part of the material stiffness is utilized for stabilization of the element stiffness matrix. A feature of the formulation is that locking behavior for nearly incompressible materials is successfully removed by the spectral decomposition of the material stiffness. The eigenvalue analysis demonstrates that the method eliminates higher energy modes associated with locking behavior for nearly incompressible materials, while capturing constant strain energy modes for both compressible and nearly incompressible materials. The convergence and accuracy of the B-bar VEM are discussed using 2D and 3D examples with various element shapes (convex and non-convex).

Original languageEnglish (US)
Pages (from-to)1423-1439
Number of pages17
Issue number6
StatePublished - Jun 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


  • B-bar method
  • Eigenvalue analysis
  • Material stiffness splitting
  • Nearly incompressible material
  • Virtual element method


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