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

TL;DR

This paper develops a flexible simulation framework combining a novel all-angle contact formulation with various geometrically exact beam elements, enabling accurate modeling of fiber-based materials and structures with different geometries and load conditions.

Contribution

It introduces a new Simo-Reissner beam element with Hermite interpolation and combines it with the ABC contact formulation, extending applicability to complex slender beam problems.

Findings

Demonstrates convergence and locking avoidance of the new beam element.

Shows the modular framework's effectiveness for diverse fiber-based applications.

Validates the contact scheme's robustness across different beam models.

Abstract

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.