Rheological models for elasto-plastic behavior of superconducting strands

The main scope of this paper is to present rheological models that can simulate the non-linear behavior of superconducting strands at different temperatures. In detail, these models estimate the values of the elastic modulus (E) and the elastic-plastic tangent modulus (H) in a very simple and efficient way. Superconducting strands are composite materials; they are usually made of a normal metal matrix where superconducting filaments are embedded. 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 single springs, because of their elastic behavior. With respect to the transversal plane, two models are developed. In the first one all materials are considered as a composition of systems of mechanisms (springs and frictional devices) arranged in series. In the second one, which is more accurate, the cross section of the wire is subdivided into different stripes. Each stripe is represented again by a composition of mechanisms and is considered in parallel with the other stripes. Different wires are taken into consideration and their elastic modulus and elastic-plastic tangent modulus are obtained. The three models developed for each strand are compared with numerical results obtained in previous works with the finite element method and virtual testing technique.