Kevin Jacques

Inclusion of a Direct and Inverse Energy-Consistent Hysteresis Model in Dual Magnetostatic Finite-Element Formulations

This paper deals with the implementation of an energy-consistent ferromagnetic hysteresis model in 2-D finite-element computations. This vector hysteresis model relies on a strong thermodynamic foundation and ensures the closure of minor hysteresis loops. The model accuracy can be increased by controlling the number of intrinsic cell components, while parameters can be easily fitted on common material measurements. Here, the native h-based material model is inverted using the Newton-Raphson method for its inclusion in the magnetic vector potential formulation. Simulations are performed on a 2-D T-shaped magnetic circuit exhibiting rotational flux. By way of validation, the results are compared with those obtained with the dual magnetic scalar potential formulation. A very good agreement for global quantities is observed.

Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems using Magnetic Induction Conforming Formulations

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.

Representation of microstructural features and magnetic anisotropy of electrical steels in an energy-based vector hysteresis model

This paper demonstrates how the statistical distribution of pinning fields in a ferromagnetic material can be identified systematically from standard magnetic measurements, Epstein frame or Single Sheet Tester (SST). The correlation between the pinning field distribution and microstructural parameters of the material is then analyzed.

Comparison between differential and variational forms of an energy-based hysteresis model

This paper compares two implementations of an energy-based ferromagnetic hysteresis model for finite element computations. The first implementation is an approximated explicit solution of the non-linear differential equation that is obtained from the energy balance of the magnetic material. The second implementation borrows from the theory of plasticity a variational formulation to solve exactly this differential equation. Both implementations are quantitatively compared in terms of accuracy and computational cost. The differential approach turns out to be much faster than the variational one and to give in most situations a result very close to that of the exact variational approach.