Simulation by Finite Difference Numerical Method of ${\rm Nb}_{3}{\rm Sn}$ Strand Under Bending Strain

We report on the simulation of the current distribution in Nb₃Sn strand subjected to pure bending strain, obtained by resolving the implicit diffusion equations with finite difference algorithm in Mathworks environment. The critical current dependence on bending, temperature, and magnetic field is modeled by the Improved Deviatoric Scaling Law and is used in the power law electric field dependence across the superconductor. The strand is discretized in elements representing groups of twisted filaments embedded in the stabilization matrix and a distributed constant circuit model is applied for current transfer among filament bundles. The code is preliminarily validated by comparison with analytical solutions for different simplified situations, each one corresponding to a proper boundary condition. Transverse matrix resistivity and twist-pitch values are crucial elements for matching numerical results with experimentally measured critical currents.