Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures

摘要

Recently, the authors have proposed a novel all-angle beam contact (ABC)formulation that combines the advantages of existing point and line contactmodels in a variationally consistent manner. However, the ABC formulation hasso far only been applied in combination with a special torsion-free beam model,which yields a very simple and efficient finite element formulation, but whichis restricted to initially straight beams with isotropic cross-sections. Inorder to abstain from these restrictions, the current work combines the ABCformulation with a geometrically exact Kirchhoff-Love beam element formulationthat is capable of treating even the most general cases of slender beamproblems in terms of initial geometry and external loads. While the neglect ofshear deformation that is inherent to this formulation has been shown toprovide considerable numerical advantages in the range of high beam slendernessratios, alternative shear-deformable beam models are required for examples withthick beams. The current contribution additionally proposes a novelgeometrically exact beam element based on the Simo-Reissner theory. Similar tothe torsion-free and the Kirchhoff-Love beam elements, also this Simo-Reissnerelement is based on a C1-continuous Hermite interpolation of the beamcenterline, which will allow for smooth contact kinematics. For this HermitianSimo-Reissner element, a consistent spatial convergence behavior as well as thesuccessful avoidance of membrane and shear locking will be demonstratednumerically. All in all, the combination of the ABC formulation with thesedifferent beam element variants (i.e.~the torsion-free element, theKirchhoff-Love element and the Simo-Reissner element) results in a veryflexible and modular simulation framework that allows to choose the optimalelement formulation for any given application in terms of accuracy, efficiencyand robustness.