Cable deformation simulation and a hierarchical framework for Nb3Sn Rutherford cables

Knowledge of the three-dimensional strain state induced in the superconducting filaments due to loads on Rutherford cables is essential to analyze the performance of Nb3Sn magnets. Due to the large range of length scales involved, we develop a hierarchical computational scheme that includes models at both the cable and strand levels. At the Rutherford cable level, where the strands are treated as a homogeneous medium, a three-dimensional computational model is developed to determine the deformed shape of the cable that can subsequently be used to determine the strain state under specified loading conditions, which may be of thermal, magnetic, and mechanical origins. The results can then be transferred to the model at the strand/macro-filament level for rod restack process (RRP) strands, where the geometric details of the strand are included. This hierarchical scheme can be used to estimate the three-dimensional strain state in the conductor as well as to determine the effective properties of the strands and cables from the properties of individual components. Examples of the modeling results obtained for the orthotropic mechanical properties of the Rutherford cables are presented.