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The purpose of this article is to estimate the magnetic field dependent critical current density scaling relation of NbTi used in a superconducting wire. The estimation problem is set using a finite element method based forward model solving the critical current of a wire in external magnetic fields. A sensitivity analysis is carried out to reveal the uncertainties in the process. It is shown that the methods provide accurate predictions of critical currents in a wire, but there are uncertainties related to the zero-field critical current density of the material. [ABSTRACT FROM AUTHOR]

The use of the classical finite element method (FEM) to solve problems with magnetic composites leads to huge linear systems that are impossible to solve. Instead, homogenization and multiscale methods are often used with the composite material replaced by a homogeneous material with the homogenized constitutive law obtained by solving cell-problems representing the mesoscale material structure. For non-linear time-dependent problems, FEM is often used with a time-transient method (TTM) and the solution is obtained one time-step at a time. However, in cases where a steady-state solution is of interest, the multiharmonic method can be faster and more cost effective for the same accuracy of the time discretization. In addition, when solving magnetoquasistatic multiscale problems with TTM, the dynamic hysteresis in the homogenized fields can slow down or even impede the convergence of the macro-scale problem due to the possibly non-continuously differentiable homogenized material laws. This work presents a novel robust modelling approach for non-linear magnetoquasistatic problems combining multiharmonic method with the multiscale method. [ABSTRACT FROM AUTHOR]