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

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.