Analysis Of Magnetic Flux And Vortex Characteristics Of Type-Ⅱ Superconducting Materials Under Mechanical Deformation

Superconducting materials which are well known to exhibit fascinating advantages of zero resistivity and Meissner effect within the tetrahedral parameter space determined by the critical magnetic field, the critical temperature and the critical current density have a very extensive and important engineering applications and prospect. However, superconducting materials usually work in the extreme low temperature and electromagnetic environment which accompany with the volume decreasing and mechanical deformation, and plenty of researches demonstrated that mechanical deformation of superconducting materials have a significant effect on the superconducting properties such as the critical current density, the critical temperature and so on.In this study, the time-dependent Ginzburg-Landau (TDGL) theory is used for investigating superconducting magnetic properties of type-Ⅱ superconducting materials under mechanical deformation in an applied magnetic field. The magnetic flux and vortex characteristics and behavior related to the deformed superconducting materials are obtained. By means of the manipulation of the mixed variational principle with independent variations of the order parameter, the magnetic potential, and the displacement, all governing equations and boundary conditions of type-Ⅱ superconducting materials under mechanical deformation are derived. A finite element simulation approach was further developed to analyze the problem related to magnetic flux and vortex characteristics and behavior of type-Ⅱ superconducting materials. Firstly, the finite element numerical approach for a half-plane superconductor is performed to capture the order parameter dependence on the elastic deformation and applied magnetic field by solving the time-dependent Ginzburg-Landau (TDGL) equations. At the same time, the effects of the elastic deformation and applied magnetic field on the total energy are discussed. The results show that the pre-strains and applied magnetic fields have a significant impact on the property and energy of deformable superconducting materials. Then the nonlinear and coupled TDGL equations and elastic field governing equation are solved to obtain the order parameter, the magnetic potential and the strain for a deformable infinite superconductor with restriction at edges under applied magnetic fields. The effects of applied magnetic fields on the all different kinds of energies including the superconducting energy, the magnetic energy, the elastic energy, the interaction energy of superconductivity and magnetic, the interaction energy of superconductivity and elastic, and the total energy density are discussed in detail. Meanwhile the effects of the coupling parameter on the order parameter, the magnetic potential, the strain and the energy are also revealed. The results showed that the deformation caused by the interaction of the superconducting condensate with deformations of the crystal lattice cannot be ignored in the deformable superconducting materials. The order parameter decreases with applied magnetic field increasing, but the strain have the opponent variation. The coupling effect has a certain influence on the order parameter, the strain, and total energy of superconducting materials. Finally, the magnetic flux vortex dynamics in a two-dimensional superconducting thin plate with a hole have been demonstrated numerically, the effect of deformation and stress concentration on the superconducting properties and the vortex dynamical behavior are revealed. The results showed that the pre-strain has a remarkable influence on the flux vortex distribution and the vortex dynamics. The axle of the ellipse holes effect not only the number of vortices but also the steady configuration of vortex.