A novel finite-strain mixed isogeometric collocation formulation for hyperelastic geometrically exact beams

We propose a novel finite-strain, mixed isogeometric collocation formulation for hyperelastic geometrically exact beams. The model supports general three-dimensional hyperelastic materials and reconstructs the cross-sectional deformation without any modification of the fundamental kinematic assumption typically employed for geometrically exact beams. We express the finite strain components in terms of the one-dimensional geometrically exact strain measures, which allows to exploit existing SO(3)-consistent linearization procedures developed for linearly elastic materials. The governing equations in the strong form are discretized using the isogeometric collocation method (IGA-C). Through various numerical examples, we demonstrate the capability of the model to reproduce both large deformations and finite strains, including the cross-sectional ones, without introducing additional kinematic unknowns.