An objective and path-independent 3D finite-strain beam with least-squares assumed-strain formulation

P. Areias, M. Pires, N. Vu Bac, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


An all-encompassing finite-strain representation of rods, shells and continuum can share a common kinematic/constitutive framework where specific conditions for strain, stress and constitutive updating are applied. In this work, finite strain beams are under examination, with several classical requirements met by cooperative techniques judiciously applied. Specifically: the use of a continuum constitutive law is possible due to the relative strain formulation previously introduced, the rotation singularity problem is absent due to the use of a consistent (quadratic) updated Lagrangian technique. Objectiveness and path-independence of director interpolation are satisfied due to the use of a Löwdin frame. These properties are proved in this work. Moreover, high coarse-mesh accuracy is introduced by the least-squares assumed-strain technique, here specialized for a beam. Examples show the accuracy and robustness of the formulation.

Original languageEnglish
Pages (from-to)1115-1131
Number of pages17
JournalComputational Mechanics
Issue number4
Publication statusPublished - 2019 Oct 1

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.


  • Assumed strains
  • Constitutive laws
  • Geometrically exact beams
  • Least-squares
  • Nonlinear

ASJC Scopus subject areas

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


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