Magnetostrictive behaviour of thin superconducting disks

TL;DR

This paper analyzes the magnetostrictive behavior of thin superconducting disks under magnetic fields, deriving stress and strain distributions based on flux pinning and the Bean model, revealing maximum tensile stress points.

Contribution

It provides a comprehensive analytical framework for stress and strain in thin superconducting disks considering flux pinning and magnetostriction effects.

Findings

Maximum tensile stress occurs midway between maximum field and remanent state.

Derived formulas for stress, strain, and magnetostriction in thin disks.

Established relationship between maximum stress and peak magnetic field.

Abstract

Flux-pinning-induced stress and strain distributions in a thin disk superconductor in a perpendicular magnetic field is analyzed. We calculate the body forces, solve the magneto-elastic problem and derive formulas for all stress and strain components, including the magnetostriction $\Delta R/R$. The flux and current density profiles in the disk are assumed to follow the Bean model. During a cycle of the applied field the maximum tensile stress is found to occur approximately midway between the maximum field and the remanent state. An effective relationship between this overall maximum stress and the peak field is found.