Computation of Strain State in a ${\rm Nb}_{3}{\rm Sn}$ Strand Using Nonlinear Hierarchical Models

The large range of length scales present within accelerator magnets suggests the incorporation of a hierarchical structure into computational models. Evaluation of the strain state present within the superconducting filaments is necessary in order to determine the critical current of Nb₃Sn based magnets. As part of an ongoing investigation at LBNL, a three-dimensional nonlinear multiscale model is developed to investigate the behavior of Nb₃Sn strands. The strain state in the superconducting filaments is examined by simulating a cool down from reaction to 4.2 K. The effects of strand geometry on the final strain state are also explored. The validity of the model is tested through the comparison of the predicted moduli to experimental tangent measurements.