Introduction of Nonlinear Properties Into Hierarchical Models of ${\rm Nb}_{3}{\rm Sn}$ Strands

The development of computational models representing Rutherford cable formation and deformation is necessary to investigate the strain state in the superconducting filaments in Nb3Sn magnets. The wide variety of length scales within accelerator magnets suggests usage of a hierarchical structure within the model. As part of an ongoing investigation at LBNL, a three-dimensional simplified nonlinear multiscale model is developed as a way to extend previous linear elastic versions. The inclusion of plasticity models into the problem formulation allows an improved representation of strand behavior compared to the linear elastic model. This formulation is applied to a single Nb
₃
Sn strand to find its effective properties as well as the strain state in the conductor under loading.