Flux-pinning-induced stress and strain in superconductors: Long rectangular slab

Abstract

The flux-pinning-induced magnetostriction of hard type-II superconductors shaped as a rectangular slab is analyzed. An exact solution of the magnetoelastic three-dimensional problem is found using the plane strain approach. All stress and strain components are expressed in terms of the flux-density profile in the slab, and apply for any critical-state model ${j}_{c}{=j}_{c}(B).$ Discussed at some length is the tensile stress occurring for a descending magnetic field. Results for both the Bean model and the exponential model are presented.