The Microstructural Model of the Ferromagnetic Material Behavior in an External Magnetic Field

Abstract

In this paper, the behavior of a ferromagnetic material is considered in the framework of microstructural modeling. The equations describing the behavior of such material in the magnetic field, are constructed based on minimization of total magnetic energy with account of limitations imposed on the spontaneous magnetization vector and scalar magnetic potential. This conditional extremum problem is reduced to the unconditional extremum problem using the Lagrange multiplier. A variational (weak) formulation is written down and linearization of the obtained equations is carried out. Based on the derived relations a solution of a two-dimensional problem of magnetization of a unit cell (a grain of a polycrystal or a single crystal of a ferromagnetic material) is developed using the finite element method. The appearance of domain walls is demonstrated, their thickness is determined, and the history of their movement and collision is described. The graphs of distributions of the magnetization vector in domains and in domain walls in the external magnetic field directed at different angles to the anisotropy axis are constructed and the magnetization curves for a macrospecimen are plotted. The results obtained in the present paper (the thickness of the domain wall, the formation of a 360-degree wall) are in agreement with the ones available in the current literature.

Identification of Material Properties and Optimal Design of Magnetically Shielded Rooms

“…It is well known that the magnetic field H at an arbitrary point of the space can be expressed as the sum of the external magnetic field H 0 and the contribution of the magnetized bodies H m [17]:…”

Microstructural Model of Magnetic and Deformation Behavior of Single Crystals and Polycrystals of Ferromagnetic Shape Memory Alloy

“…In this case, we solve the Euler-Ostrogradsky equation, which corresponds to the minimum of this functional, or this functional is minimized directly. This approach was implemented in [12] to describe the evolution of the magnetization and to perform a numerical simulation of the motion and interaction of the Neel domain walls in a Ni 2 MnGa single crystal under the action of a magnetic field. The second approach uses the Landau-Lifshitz-Gilbert equation and is implemented in [13] to describe the behavior of the twinned variant of martensite, which has a more complex structure compared to the one considered in [12].…”

Three-Dimensional Imaging of Metallic Grain by Stacking the Microscopic Images

“…At this point, if a strong external magnetic field is applied and then removed, residual magnetization occurs. A similar fault signal is generated, in which magnetic particles are adsorbed even in non-defective areas due to residual magnetization [22][23][24]. Even though the deformation caused by an external force causes the magnetic moment inside the magnetic domain to be anisotropic in a specific direction and, therefore, residual magnetization occurs even if an external magnetic field is not applied [25][26][27].…”