Disclosed are induction heating cells comprising tensioning members with non-magnetic metal cores. Also disclosed are methods of operating such cells, for example, to process composite parts. The non-magnetic metal cores of the tensioning members provide excellent tensile strength. Furthermore, the non-magnetic metal cores allow forming long tensioning members leading to large induction heating cells for processing large composite parts, such aircraft fuselage parts, wing parts, and the like. The diameter of these non-magnetic metal cores is less than the induction heating threshold for magnetic fields used during operation of the cells, which ensures limited or no interaction of the cores with the magnetic fields. The cores can be arranged into a tensioning member extending through and compressing the die of an induction heating cell. When multiple cores are used, these cores are electrically insulated from each other, e.g., using an insulating shell or spacing these cores away from each other.