In this paper, we present a discrete formulation of nonlinear shear- and
torsion-free rods based on \cite{gebhardt_2021_beam} that uses isogeometric
discretization and robust time integration. Omitting the director as an
independent variable field, we reduce the number of degrees of freedom and
obtain discrete solutions in multiple copies of the Euclidean space
(R3), which is larger than the corresponding multiple
copies of the manifold \left(\mathbb{R}^3 \cross S^2\right) obtained with
standard Hermite finite elements. For implicit time integration, we choose a
hybrid form of the mid-point rule and the trapezoidal rule that preserves the
linear angular momentum exactly and approximates the energy accurately. In
addition, we apply a recently introduced approach for outlier removal
\cite{hiemstra_outlier_2021} that reduces high-frequency content in the
response without affecting the accuracy, ensuring robustness of our nonlinear
discrete formulation. We illustrate the efficiency of our nonlinear discrete
formulation for static and transient rods under different loading conditions,
demonstrating good accuracy in space, time and the frequency domain. Our
numerical example coincides with a relevant application case, the simulation of
mooring lines