Abstract: Superconducting sub-cables, hierarchically twisted from multiple superconducting wires, serve as the core load-bearing units of superconducting magnets, and their mechanical properties directly determine the operational stability and long-term service reliability of superconducting magnet systems. Serving in extreme environments with ultra-low temperature, strong magnetic field and high current, superconducting sub-cables are continuously subjected to cyclic electromagnetic loads. Cyclic electromagnetic loads change the interfacial frictional contact state between wires, induce local stress concentration and damage of superconducting filaments, and simultaneously drive the sub-cable to undergo compressive deformation accompanied by stick-slip bending behavior. Existing studies are incapable of fully characterize the nonlinear stick-slip bending behavior caused by interfacial friction under electromagnetic loads. In this work, a theoretical model for the stick-slip bending behavior of superconducting sub-cables under electromagnetic loads is established. The influence mechanism of key parameters such as electromagnetic load and the Coulomb friction coefficient on the stick-slip transition law is systematically revealed. Furthermore, the nonlinear bending response and the evolution of local frictional contact behavior of sub-cables under electromagnetic load-unload process are quantitatively characterized based on the plastic incremental theory. The results indicate that electromagnetic loads enhance the interfacial friction between wires and dominate the stick-slip bending behavior of sub-cables. In the process of cyclic bending, inter-wire friction directly determines the energy dissipation and critical bending curvature of sub-cables, and the friction coefficient imposes a nonlinear regulation effect on energy dissipation. Although high friction force can effectively restrain the relative slip of wires, it inevitably aggravates cyclic energy loss. The results indicate that sub-cable design needs to balance anti-slip capability and the requirement of low mechanical energy loss. Synergistic control of interfacial friction and pre-tensile loads can realize the optimization of the service performance of sub-cables.