Analysis of bending stiffness in multi-stage superconducting cable

•A modified theoretical model is proposed to study the bending stiffness of the superconducting cable with multi-stage structure.•A full 3D finite element model has been developed to validate the theoretical model for the bending stiffness problems.•The bending stiffness of multi-stage superconducting cables were systematically investigated. Superconducting cables with multi-stage structures are used in the ITER magnets. Here we propose a theoretical model focusing on the bending behavior of superconducting cable. On the basis of the analysis of the effective Young's moduli and curvature radius, the bending stiffnesses of multi-stage superconducting cables are obtained theoretically. The dependence of the bending stiffness on the helical pitch at different hierarchical structure is examined. With the aid of the finite element approach and a simple experiment, the theoretical model can be validated by comparing the theoretical solutions and numerical and experimental results. The theoretical predictions are in good agreement with the numerical and experimental results. The results show that the proposed model can successfully analyze the bending stiffnesses of the multi-stage superconducting cables. This theoretical model can be utilized to optimize the bending stiffnesses of the multi-stage superconducting cables, by tuning the helical pitch of the cables.