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The paper proposes a 3D extension of the linear tensor model of magnetic permeability for axially anisotropic materials. In the proposed model, all phases of a magnetization process are considered: linear magnetization, magnetization rotation, and magnetic saturation. The model of the magnetization rotation process is based on the analyses of both anisotropic energy and magnetostatic energy, which directly connect the proposed description with physical phenomena occurring during a magnetization process. The proposed model was validated on the base of previously presented experimental characteristics. The presented extension of the tensor description of magnetic permeability enables the modelling of inductive devices with cores made of anisotropic magnetic materials and the modelling of magnetic cores subjected to mechanical stresses. It is especially suitable for finite element modelling of the devices working in a magnetic saturation state, such as fluxgate sensors.

Highly sensitive fluxgate magnetic field sensors with rod-shaped cores are widely used for non-destructive testing as well as for industrial applications. However, in case of both Foerster and Vacquier (two-core sensors configurations), fluxgate sensors sensitivity is directly connected with the relative magnetic permeability of the sensor’s core. It should be highlighted that the magnetic permeability of rod-shaped magnetic cores is driven mainly by the demagnetization factor determined by its slenderness (aspect ratio). The paper presents the analyses of sensitivity limits of fluxgate sensors with rod-shaped cores. On the base of estimations of demagnetization factor specific for fluxgate sensors, it is shown that in case of rod-shaped cores, the sensor’s sensitivity is connected with the shape of the core rather than its relative magnetic permeability. This conclusion is essential during the development and optimization of functional characteristics of fluxgate sensors.

Tetrahedral meshing is the critical element of finite element modeling. Recently, adaptive meshing has been commonly used. In such meshing, according to the Delaunay method, mesh density is connected with the curvature of modeled object’s edge. Such a method is especially efficient during the modeling of mechanical systems. However, the efficiency of commonly used meshing algorithms is strongly limited in surface-focused phenomena, such as eddy current induced by magneto-dynamic processes. The paper proposes the improved method of Delaunay meshing considering the specific requirements of magnetodynamic systems. In the proposed method, tetrahedral mesh density may be flexibly modified according to the needs of modeled physical phenomena, such as eddy current density. As a result, physical effects may be efficiently and accurately described in finite element models. The paper presents the example of implementing the proposed solution for cylindrical wire. The complete source code is available as open-source software for further practical use and development.