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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.

In this article, based on the theory of micromagnetism, a microstructural model of the behavior of the Heusler alloy in a magnetic field is constructed. The dynamics of the magnetic process is described by the Landau–Lifshitz–Gilbert equation. Using the Galerkin procedure, variational equations corresponding to the differential relations of the magnetic problem are written out. For numerical simulation, we consider the problem of magnetization of a Ni2MnGa alloy polytwin crystals, each grain of which is a twinned variant of martensite and has pronounced anisotropic properties. First, we consider the process of magnetization of a single grain, when an external magnetic field is applied at different angles to the anisotropy axes of twinned variants, and then, based on the results obtained, we plot magnetization curves for various (isotropic and texture-oriented) polycrystalline samples. This paper does not consider the process of detwinning, which can occur in such a material during the magnetization at a sufficiently high external field strength.

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