Magnetic-thermal-mechanical coupling behavior simulation for a porous high-temperature superconductor based on fractal derivatives

In this paper, the magnetic-thermal-mechanical coupling behavior for a porous high-temperature superconductor placed in a pulsed field is studied numerically within the framework of finite element analysis and based on fractal derivatives. Firstly, as a kind of oxide ceramic material, the porous properties of high-temperature superconductors (SCs) are characterized through fractal methods. Then, we obtained the Maxwell equation and heat conduction equation in the form of fractal derivatives, and thus the difficulties brought by the multi connectivity of materials to finite element (FEM) modeling can be overcome. The FEM simulation results indicate that the porous properties have a significant impact on the maximum trapped magnetic field, surface temperature of superconductors, and maximum stress inside superconductors. The presented method can also provide a more efficient solution for the multi-field coupling simulation of other porous electromagnetic media.