On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials

Osman Gültekin, Hüsnü Dal, Gerhard Holzapfel

Research output: Contribution to journalArticlepeer-review


Quasi-incompressible behavior is a desired feature in several constitutive models within the finite elasticity of solids, such as rubber-like materials and some fiber-reinforced soft biological tissues. The Q1P0 finite element formulation, derived from the three-field Hu–Washizu variational principle, has hitherto been exploited along with the augmented Lagrangian method to enforce incompressibility. This formulation typically uses the unimodular deformation gradient. However, contributions by Sansour (Eur J Mech A Solids 27:28–39, 2007) and Helfenstein et al. (Int J Solids Struct 47:2056–2061, 2010) conspicuously demonstrate an alternative concept for analyzing fiber reinforced solids, namely the use of the (unsplit) deformation gradient for the anisotropic contribution, and these authors elaborate on their proposals with analytical evidence. The present study handles the alternative concept from a purely numerical point of view, and addresses systematic comparisons with respect to the classical treatment of the Q1P0 element and its coalescence with the augmented Lagrangian method by means of representative numerical examples. The results corroborate the new concept, show its numerical efficiency and reveal a direct physical interpretation of the fiber stretches.
Original languageEnglish
Pages (from-to)443-453
Number of pages11
JournalComputational Mechanics
Publication statusPublished - 2019


  • Finite element analysis
  • Augmented Lagrangian method
  • Hyperelasticity
  • Quasi-incompressibility
  • Fiber-reinforced materials
  • Soft biological tissues


Dive into the research topics of 'On the quasi-incompressible finite element analysis of anisotropic hyperelastic materials'. Together they form a unique fingerprint.

Cite this