This work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based on the theory of Cosserat rods, where the static equilibrium is calculated by minimizing the linear elastic energy. For this algorithmic approach, in each iteration the static equilibrium is obtained by minimizing the potential energy with locally constant algorithmic bending stiffness values. These constants are updated according to the given nonlinear elastic constitutive law until the state of the rod converges. To determine the nonlinear elastic constitutive bending behavior of the flexible slender structures (such as cables) from the measured values, we formulate an inverse problem. By solving it we aim to determine a curvature-dependent bending stiffness characteristic and the reference curvatures using the given measured values. We first provide examples using virtual bending measurements, followed by the application of bending measurements on real cables. Solving the inverse problem yields physically plausible results.

This contribution aims to model and characterize the nonlinear elastic behavior of hoses under internal pressure. A highly resolved 3D continuum model is used to identify relevant effects of preformed hoses under internal pressure. The focus of this work is on the Bourdon effect, which is illustrated by simulating two simplified models, a full torus and a quarter torus. For a full torus, the Bourdon effect can be observed by the fact that the radius of curvature increases in addition to the expansion of the cross-sectional radius. For a quarter torus, which is a simplified example of a curved hose, the Bourdon effect can be observed by the tendency of the hose to straighten under internal pressure. Furthermore it is detected for both examples that the non-constant distribution of the poloidal (hoop) stress over the cross-section leads to an ovalization behavior. In addition, the model of a quarter torus is extended to a more complex model with straight hose sections at both ends.