Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping

Kenji Takizawa*, Tayfun E. Tezduyar, Takafumi Sasaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


We derive a hyperelastic shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid–structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the “midsurface” location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the “midsurface” location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung’s models, for the compressible- and incompressible-material cases, and for two different locations of the “midsurface.” We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.

Original languageEnglish
Pages (from-to)681-700
Number of pages20
JournalComputational Mechanics
Issue number4
Publication statusPublished - 2019 Apr 15


  • Artery
  • Fung’s material model
  • Hyperelastic material
  • Isogeometric discretization
  • Kirchhoff–Love shell theory
  • Neo-Hookean material model
  • Out-of-plane deformation mapping

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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