Efficient strain-gradient mixed elements using shared degrees of freedom for the discretised fields

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

A displacement-only finite-element formulation of strain-gradient models requires elements with C1 continuous interpolation. Mixed formulations have been proposed to allow the use of more common C0 element shape functions. These mixed formulations are based on the interpolation of two different fields, displacement and some kind of displacement gradient, with the relation between the two fields enforced using either Lagrange multipliers or penalty methods. All elements proposed in the literature for such formulations use a distinct set of degrees of freedom to discretise each field. In this work, we introduce for the first time shared degrees of freedom, that lead to a mixed formulation with a significantly better numerical performance. We describe how this novel mixed formulation can be derived, present individual elements implementing this, and discuss the significance of the results.
Original languageEnglish
Article numbere7536
JournalInternational Journal for Numerical Methods in Engineering
Early online date23 May 2024
DOIs
Publication statusE-pub ahead of print - 23 May 2024

Keywords / Materials (for Non-textual outputs)

  • finite elements
  • mixed formulation
  • shared degrees of freedom
  • strain-gradient

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