Magneto-Elastic-Plastic Buckling/Snapping and Bending of Cantilever Ferromagnetic Rectangular Plates

The magnetic interactions with deformable bodies are every-day phenomena in modern technologies. The understanding of the magneto-elastic-plastic bending and stability of the ferromagnetic beam [xxx] plate and shell structures under the strong magnetic field is quite crucial and helpful in engineering applications, for example, in the design and control of fusion reactors, micro-electronics, magnetic lévitation, and magneto- formation techniques, etc. This paper presents an analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever soft ferromagnetic rectangular plates. Based on the expression of magnetic force from the variational principle of ferromagnetic plates, the buckling and bending theory of thin plates, the Mises yield criterion and the increment theory for plastic deformation, here, we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-coupling problems by the finite element method. Along with that the phenomena of buckling/snapping and bending, or the characteristic curve of deflection versus magnitude of applied magnetic fields are numerically displayed, the critical values of buckling/snapping, and the influences of plastic deformation and the width of plate on the critical values of buckling/snapping of ferromagnetic plates, the plastic regions expanding with the magnitude of applied magnetic field, as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.