  Recently, the authors have proposed a novel all-angle beam contact (ABC)
formulation that combines the advantages of existing point and line contact
models in a variationally consistent manner. However, the ABC formulation has
so far only been applied in combination with a special torsion-free beam model,
which yields a very simple and efficient finite element formulation, but which
is restricted to initially straight beams with isotropic cross-sections. In
order to abstain from these restrictions, the current work combines the ABC
formulation with a geometrically exact Kirchhoff-Love beam element formulation
that is capable of treating even the most general cases of slender beam
problems in terms of initial geometry and external loads. While the neglect of
shear deformation that is inherent to this formulation has been shown to
provide considerable numerical advantages in the range of high beam slenderness
ratios, alternative shear-deformable beam models are required for examples with
thick beams. The current contribution additionally proposes a novel
geometrically exact beam element based on the Simo-Reissner theory. Similar to
the torsion-free and the Kirchhoff-Love beam elements, also this Simo-Reissner
element is based on a C1-continuous Hermite interpolation of the beam
centerline, which will allow for smooth contact kinematics. For this Hermitian
Simo-Reissner element, a consistent spatial convergence behavior as well as the
successful avoidance of membrane and shear locking will be demonstrated
numerically. All in all, the combination of the ABC formulation with these
different beam element variants (i.e.~the torsion-free element, the
Kirchhoff-Love element and the Simo-Reissner element) results in a very
flexible and modular simulation framework that allows to choose the optimal
element formulation for any given application in terms of accuracy, efficiency
and robustness.
