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

Kyoungsoo Park, Heng Chi, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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
Pages (from-to)1423-1439
Number of pages17
Issue number6
Publication statusPublished - 2021 Jun

Bibliographical note

Funding Information:
KP acknowledges the supports from the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (Grant Number: 2018R1A2B6007054), and from the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by the Ministry of Trade, Industry & Energy (Grant Number: 20174030201480). HC and GHP acknowledge support from the US National Science Foundation (NSF) under Grant #1624232 (formerly #1437535), and the support from the Raymond Allen Jones Chair at the Georgia Institute of Technology.

Publisher Copyright:
© 2020, Springer Nature B.V.

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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