Ferromagnetic composite materials are widely used in electrical devices to guide magnetic fluxes. They consist of a magnetic and conductive phase, electrically insulated from each other by a dielectric material, which helps reduce eddy-current losses. Historically, stacks of laminations were the preferred solution for manufacturing magnetic cores. However, the emergence of soft magnetic composites (SMCs) has enabled the development of new electrical devices with fully three-dimensional topologies. To improve the energy efficiency of converters incorporating magnetic materials, it is essential to develop fast and accurate numerical models capable of estimating losses within their magnetic cores in order to minimize them.
The finite element (FE) method is the most commonly used approach for studying ferromagnetic composite materials with complex geometries and nonlinear behavior. Numerous formulations have been proposed to address the challenges inherent to Maxwell’s equations in the magnetoquasistatic (MQS) regime, including nonlinear constitutive laws, gauge conditions required to ensure uniqueness of the solution, coupling with external electrical circuits, etc.
[1]. When composites are involved, this method is often combined with homogenization techniques to reduce the computational cost that would result from a solution with a fine mesh of the material microstructure. In this context, the Heterogeneous Multiscale Method (HMM), known as FE2 in the mechanics community, is widely used and provides excellent results for multiscale problems when the scale-separation assumption is satisfied [2]. This approach has
already been implemented by researchers involved in the supervision of this internship. Homogenization techniques have been developed at the Grenoble Electrical Engineering Laboratory (G2Elab) to address MQS problems in laminated cores.The objective of this internship is to develop finite element-based numerical models for low- frequency electromagnetic problems using the open-source MFEM platform [3, 4], and to use these models to implement a multiscale model for a 2D MQS problem.
References
[1] G. Meunier, , The Finite Element Method for Electromagnetic Modeling, Wiley & Sons, 2008.
[2] J. Yvonnet, Computational Homogenization of Heterogeneous Materials with Finite Elements. Springer, 2019.
[3] R. Anderson, et al., MFEM: A Modular Finite Element Methods Library, Comput. Math. Appl. 81 (2021): 42-74.
[4] MFEM (https://mfem.org/).
