Efficient simulation of bending behavior of spiral strands : a strategy based on computational homogenization

A spiral strand is a multilayer cable with each layer consisting of helically shaped wires. These strands are widely used in many different engineering applications, such as anchorage in offshore engineering and power transmission lines. These strands exhibit axial-torsional and axial-bending coupling due to their helical geometry. The axial-torsional coupling can be considered linear, as it is largely governed by the geometry of the strand, while the axial-bending coupling is highly non-linear, as it results from the frictional interactions between the layers.To the best of the author's knowledge, so far, only the simplest possible axial-bending loading case, i.e., uniaxial bending under constant axial force, has been studied experimentally, numerically and analytically for the spiral strands in the literature. However, in real life situations, the spiral strands are usually subjected to biaxial bending and variable axial force. Therefore, the main objective of the current thesis has been to numerically characterize the macroscopic (the moment curvature response) and microscopic (the axial force of individual wires) behaviors of these strands under these loading conditions, which has been achieved in several steps.For this purpose, as the first step, the in-house finite element code, Multifil, has been verified against the available experimental data for the axial-torsional and axial-bending experiments, to support its use as a predictive tool to analyze the behavior of spiral strands. For this verification step, all wires and frictional contact interactions have been modeled explicitly.Next, a computational homogenization framework for spiral strands has been developed. The benefits of developing a homogenization framework are twofold: first, it shows that a spiral strand can be replaced by a single beam with an effective material properties, and second, it provides a virtual experimental platform to perform experiments that have not yet been performed in real life. The proposed homogenization framework has been verified with the results obtained from the full-scale analysis of Multifil, which itself has been verified against experimental data.In the next step, the macroscopic behavior of spiral strands subjected to biaxial bending and variable axial force is studied thanks to the developed homogenization framework. Furthermore, a rheological constitutive model is proposed to represent the macroscopic behavior of the strands subjected to these loads. Advantages of the proposed constitutive model are its easy parameter identification and very low computational cost. The responses of the rheological model have been verified against the homogenization results.Finally, in order to predict the fatigue life of spiral strands, it is necessary to have information on the axial force of the individual wires making up the strand. For this purpose, a model is proposed that is capable of accurately predicting the axial forces of the wires when the strand is subjected to biaxial bending and variable axial force. The model, which has a very low computational cost, has been verified against the responses obtained from homogenization.In short, using the models proposed in this thesis, a spiral strand can be replaced by a single beam, while having access to both macroscopic and microscopic responses of the strand with very low computational cost. To have a rough comparison of the computational cost of the different methods, full-scale modeling of a spiral strand using Multifil can take up to a few weeks on a supercomputer (and is sometimes out of reach due to the high cost), while finding the parameters for the two proposed models to predict the macroscopic and microscopic responses of the spiral strand can take up to a few hours on a supercomputer, and solving the beam model takes a few seconds on a laptop.