over(B, -) and over(F, -) projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements

T. Elguedj*, Y. Bazilevs, V. M. Calo, T. J.R. Hughes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

308 Scopus citations


This paper presents projection methods to treat the incompressibility constraint in small- and large-deformation elasticity and plasticity within the framework of Isogeometric Analysis. After reviewing some fundamentals of isogeometric analysis, we investigate the use of higher-order Non-Uniform Rational B-Splines (NURBS) within the over(B, -) projection method. The higher-continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results. A new non-linear over(F, -) projection method, based on a modified minimum potential energy principle and inspired by the over(B, -) method is proposed for the large-deformation case. It leads to a symmetric formulation for which the consistent linearized operator for fully non-linear elasticity is derived and used in a Newton-Raphson iterative procedure. The performance of the methods is assessed on several numerical examples, and results obtained are shown to compare favorably with other published techniques.

Original languageEnglish (US)
Pages (from-to)2732-2762
Number of pages31
JournalComputer Methods in Applied Mechanics and Engineering
Issue number33-40
StatePublished - Jun 1 2008
Externally publishedYes

Bibliographical note

Funding Information:
T. Elguedj was supported by the French Délégation Générale pour l’Armement and the Centre National pour la Recherche Scientifique. Y. Bazilevs was partially supported by the J.T. Oden ICES Postdoctoral Fellowship at the Institute for Computational Engineering and Sciences. Y. Bazilevs, V.M. Calo and T.J.R. Hughes were partially supported by the Office of Naval Research under Contract No. N00014-03-0263, Dr. Luise Couchman, contract monitor, and Sandia National Laboratories under Contract No. 114166. This support is gratefully acknowledged.


  • Incompressibility
  • Isogeometric analysis
  • Non-linear elasticity
  • Plasticity
  • Volumetric locking
  • over(B, -) method
  • over(F, -) method

ASJC Scopus subject areas

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


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