A rheological approach for elasto-plastic behaviour of superconducting strands

Superconducting (SC) strands are composite materials: they are usually made of a normal metal matrix where superconducting filaments are embedded. The main purpose of this paper consists in developing a simple but effective approach based on rheological models, to simulate the global elastic-plastic behavior of SC wires. In particular, starting from Prandtl generalized scheme, the strand elastic modulus and elastic-plastic tangent modulus are obtained at different temperatures. The wire mechanics is studied by taking into consideration both the longitudinal behavior (along the axis of the wire) and the transversal one (on the plane section of the wire itself). Concerning the longitudinal axis, the constitutive materials are represented by a system of mechanisms arranged in parallel: normal metals are represented by a series of springs and frictional devices, while superconducting filaments are considered as a single spring, because of their elastic properties. Concerning the transversal behavior, the scheme is more complex, therefore the cross section is subdivided into stripes. Each stripe, which is represented by a series of springs and frictional devices, is arranged in parallel with the other ones. Finally, to show the effectiveness of the presented method, three different wires are taken into consideration and results obtained are compared with numerical ones previously calculated by means of virtual testing homogenization and finite element (FE) analysis. The presented approach allows studying the elastic- plastic behavior of complex composite materials in a simple way, without the need of FE method or the use of complex homogenization techniques.