A Multiscale Model for Superconducting Strands

This paper presents a model for the numerical analysis of the thermo-mechanical strain occurring in the multifilamentary strands of superconducting cables. The bronze route strand from Vacuumschmelze is considered, as it will be used for some of the ITER coils. This kind of elementary Nb3Sn based strand is composed of a bare copper matrix where 55 sub-groups of 85 SC filaments are inserted. Within the Finite Element technique a very fine discretisation would be needed to study the strand cross section on the fine scale material, resulting in a model too large to be solved in a reasonable amount of time. In this work an alternative approach is proposed: the macroscopic behaviour of an individual strand is studied by means of a numerical homogenized constitutive relation. The FE tools of theory of asymptotic homogenisation are here extended for the piecewise linear analysis of the superconducting fibrous composite with non-linear, temperature dependent components. We account also for local material yielding at the stage of microanalysis. Since we limit our consideration to the case of the strand, the problem of unilateral constraints can be disregarded. This problem has been already discussed and presented in one of our previous works. Two different FE models are compared to evaluate the error caused by the approximations involved in the homogenisation method. A very fine discretisation of a group of 85 SC filaments is developed, modelling the different materials of the composite, and a thermo-mechanical analysis is performed. The results are compared with those deriving from a rather coarse mesh with the homogenised constitutive relation. The error induced by the homogenisation procedure is small and this indicates that the homogenisation procedure gives acceptable results with small computational effort.