Simulation and parameterization of nonlinear elastic behavior of cables

Abstract

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.