## 1 Introduction
[15] used LS-DYNA to establish a full three-dimensional, elastic-plastic finite element model of multi-layer helical cables under a quasi-static axial load. The model uses three-dimensional solid elements to discretize each strand and simulates the contact types between all strands. The model also uses the law of non-linear hardening to explain the plastic deformation. [PERSON] et al. [16] succeeded in analyzing the flexural stiffness of the strands using a solid three-dimensional finite element model, although their research was limited to single-pitch, single-layer cables. To summarize, the method of full three-dimensional solid modeling considers the contact between wires, among other factors, which results in a large number of computations, and thus the length of a fully three-dimensional solid element finite element model is usually very short. To reduce the computational complexity of the model, some scholars have used a beam element instead of solid element to establish a finite element model of a strand. [PERSON] et al. [17] used a beam element to model a single-layer conductor and managed the contact interaction between the lines using a coupling equation between the corresponding nodes, and thus the slip between the lines was not considered. The model was applied to the analysis of strands under bending loads, which is still limited to single-layer strands with a small deflection. [PERSON] et al. [18] also modeled a conductor. Each line contact was simulated using a spring element. The stiffness of the spring element was based on the Hertzian contact theory. Although the correctness of this method has been proved, its application was still limited to single or double layers with a small displacement. [PERSON] et al. [19; 20] proposed a finite element modeling method for multi-layer steel strands under multi-axial loads. This method utilizes a beam element and a three-dimensional line contact, which greatly reduce the computational complexity of the model under the premise of ensuring a high level of accuracy. In this study, a finite element, fully three-dimensional solid modeling method was used to study the mechanical response of a steel-cored aluminum strand with a mid-phase jumper under a bending deformation. A whole model (simplifying an ACSR into a solid cylinder) and a local model (modeling according to the actual structure of an ACSR) of the mid-phase jumper were established. First, the movement of the mid-phase jumper of the tension tower under wind load was studied based on the whole finite element model, and the equivalent Young's modulus of the whole model was adjusted based on the local model. The results of the whole model were then imported into the local model, and the stress distribution of each strand of the ACSR was analyzed in detail under a bending deformation to provide guidance for the treatment measures. Therefore, the whole model and the local model complemented each other, which could reduce the number of model operations and ensure the accuracy of the results. The feasibility of this method was verified through a comparison with the results of subsequent experiments. Although this modeling method was applied to the stress and deformation analysis of a mid-phase jumper in this study, it can be used to study the bending deformation of rope structures with a complex geometry and the main bending deformation. The finite element modeling method of a mid-phase jumper presented in this paper can be implemented in any general finite element software. Abaqus (2018, Dassault Systemes Simulia Corp, Johnston, RI, USA) was also used in this study.