  In this paper, we present a discrete formulation of nonlinear shear- and
torsion-free rods introduced by Gebhardt and Romero in [20] 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 (R^3),
which is larger than the corresponding multiple copies of the manifold (R^3 x
S^2) obtained with standard Hermite finite elements. For implicit time
integration, we choose the same integration scheme as Gebhardt and Romero in
[20] that is a hybrid form of the midpoint and the trapezoidal rules. In
addition, we apply a recently introduced approach for outlier removal by
Hiemstra et al. [26] 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.
