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Multiscale Finite Element Modeling of Nonlinear Quasistatic Electromagnetic Problems Niyonzima, Innocent Doctoral thesis (2014) The effective use of composite materials in the technology industry requires the development of accurate models. Typical such materials in electrotechnical applications are lamination stacks and soft ... [more ▼] The effective use of composite materials in the technology industry requires the development of accurate models. Typical such materials in electrotechnical applications are lamination stacks and soft magnetic composites, used in the so-called magnetoquasistatic (low frequency) regime. Current homogenization models (e.g. the classical homogenization method, mean field homogenization, ...) fail to handle all the difficulties raised by the modeling of these materials, particularly taking into account the complexity of their microstructure and their nonlinear/hysteretic behaviour. In this thesis we develop a multiscale computational method which allows to effectively solve multiscale magnetoquasistatic problems. The technique is inspired by the HMM (heterogeneous multiscale method), which involves the resolution of two types of problems: a macroscale problem that captures slow variations of the overall solution, and many mesoscale problems that allow to determine the constitutive laws at the macroscale and to construct accurate local fields. Macroscale and mesoscale weak, b-conform and h-conform formulations, are derived starting from the two-scale convergence and the periodic unfolding methods. We also use the asymptotic homogenization method for deriving the homogenized linear material laws and, in the end, we derive scale transitions for bridging the scales. Numerical tests carried out in the two-dimensional case allow to validate the models. In the case of b-conform formulations, it is shown that the macroscale solution approximates well the average of the reference solution and that the resolution of the mesoscale problems allows to reconstruct accurate local fields and to compute accurate Joule losses and this, for materials with (non)linear and hysteretic behavior. Similar findings were obtained for the h-conform formulations. In both cases, the deterioration of the accuracy for mesoscale problems located near the boundary of the computational domain could be treated by defining suit- able mesoscale problems near such boundaries. The extension of the model to three-dimensional problems, to multiphysical problems and the inclusion of the mesoscale domains with a stochastic distribution of phases are also some of the possible prospects for improving this work. [less ▲] Detailed reference viewed: 288 (68 ULg)Nonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites Niyonzima, Innocent ; ; Dular, Patrick et al in IEEE Transactions on Magnetics (2014), 50(02), In this paper, a heterogeneous multiscale method technique is applied to model the behavior of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale ... [more ▼] In this paper, a heterogeneous multiscale method technique is applied to model the behavior of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale homogenization theory: a macroscale problem that captures the slow variations of the overall solution, and many mesoscale problems that allow determining the constitutive laws at the macroscale. As application, an SMC core is considered. [less ▲] Detailed reference viewed: 80 (14 ULg)Nonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites Niyonzima, Innocent ; ; Dular, Patrick et al in Proceedings of the 19th Conference on the Computation of Electromagnetic Fields (COMPUMAG2013) (2013, July) In this paper, a heterogeneous multiscale method (HMM) technique is applied to model the behaviour of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale ... [more ▼] In this paper, a heterogeneous multiscale method (HMM) technique is applied to model the behaviour of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale homogenization theory: a macroscale problem that captures the slow variations of the overall solution, and many mesoscale problems that allow determining the constitutive laws at the macroscale. As application, an SMC core is considered. [less ▲] Detailed reference viewed: 19 (7 ULg)Computational Homogenization for Laminated Ferromagnetic Cores in Magnetodynamics Niyonzima, Innocent ; ; Dular, Patrick et al in IEEE Transactions on Magnetics (2013), 49(5), 2049-2052 In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization technique based on the heterogeneous multiscale method (HMM) that includes both ... [more ▼] In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization technique based on the heterogeneous multiscale method (HMM) that includes both eddy-current and hysteretic losses at the mesoscale. The HMM comprises: 1) a macroscale problem that captures the slow variations of the overall solution; 2) many mesoscale problems that allow to determine the constitutive law at the macroscale. As application example, a laminated iron core is considered. [less ▲] Detailed reference viewed: 144 (38 ULg)A Computational Homogenization Method for the Evaluation of Eddy Current in Nonlinear Soft Magnetic Composites Niyonzima, Innocent ; Vazquez Sabariego, Ruth ; Dular, Patrick et al in Proceeding of the 9th International Symposium on Electric and Magnetic Fields, EMF 2013 (2013, April 23) The use of the soft magnetic composite (SMC) in electric devices has increased in recent years. These materials made from a metallic powder compacted with a dielectric binder are a good alternative to ... [more ▼] The use of the soft magnetic composite (SMC) in electric devices has increased in recent years. These materials made from a metallic powder compacted with a dielectric binder are a good alternative to laminated ferromagnetic structures as their granular mesoscale structure allows to significantly reduce the eddy current losses. Furthermore unlike the laminated ferromagnetic structures, SMC exhibit isotropic magnetic properties what makes them good candidates for manufacturing machines with 3D flux paths. The isotropy of the thermal conductivity also allows for a more efficient heat dissipation. The use of classical numerical methods such as the finite element method to study the behavior of SMC is computational very expensive. Indeed a very fine mesh would be required in order to capture fine scale variations i.e. variations at level of metallic grains whence the use of multiscale methods for modelling SMC. The application of multiscale method to study the behaviour of SMC is relatively recent. In (A. Bordianu et al “A Multiscale Approach to Predict Classical Losses in Soft Magnetic Composites”, IEEE Trans. Mag., vol. 48, no. 4, 2012.), the authors used a homogenization technique to compute electrical and magnetic constitutive laws on a representative volume element (RVE). These laws were then used in finite element computations. Herein, the RVE has been chosen to account for the grain- grain contact that can occur in a actual SMC structure due to the compaction process and that can lead to the appearance of macroscale eddy currents. In this paper, we will extend the computational homogenization method success- fully used for modelling the behaviour of laminated ferromagnetic cores in mag- netodynamics (I. Niyonzima et al “Computational Homogenization for Laminated Ferromagnetic Cores in Magnetodynamics”, in Proc. of the 15th Biennal Confer- ence on Electromagnetic Field Computation, 2012) to the case of SMC. The method is based on the heterogeneous multiscale method (HMM) and couples two types of problems: a macroscale problem that captures the slow variations of the overall so- lution and many microscale problems that allow to determine the constitutive laws at the macroscale. The choice of RVE will also be discussed. [less ▲] Detailed reference viewed: 113 (14 ULg)Computational Homogenization for Laminated Ferromagnetic Cores in Magnetodynamics Niyonzima, Innocent ; Vazquez Sabariego, Ruth ; et al in Proceedings of the 15th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC2012) (2012, November) In this paper, we investigate the modeling of fer- romagnetic multiscale materials. We propose a computational homogenization method based on the heterogeneous multiscale method (HMM) that includes eddy ... [more ▼] In this paper, we investigate the modeling of fer- romagnetic multiscale materials. We propose a computational homogenization method based on the heterogeneous multiscale method (HMM) that includes eddy currents and hysteretic losses at the mesoscale. The HMM comprises: 1) a macroscale problem that captures the slow variations of the overall solution; 2) many microscale problems that allow to determine the constitutive law at the macroscale. As application example, a laminated iron core is considered. [less ▲] Detailed reference viewed: 110 (20 ULg)Time-domain finite-element modelling of laminated iron cores – Large skin effect homogenization considering the Jiles-Atherton hysteresis model Vazquez Sabariego, Ruth ; Niyonzima, Innocent ; Geuzaine, Christophe et al in Proceedings of the 15th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC2012) (2012, November) This paper deals with the incorporation of the Jiles- Atherton (J-A) hysteresis model in a time-domain finite-element homogenization technique for laminated iron cores. The separate discretization of each ... [more ▼] This paper deals with the incorporation of the Jiles- Atherton (J-A) hysteresis model in a time-domain finite-element homogenization technique for laminated iron cores. The separate discretization of each lamination is avoided by using dedicated skin-effect basis functions, which also serve to interpolate the J- A hysteretic material law. As validation test case, a stacked ring core surrounded by a toroidal coil is considered. [less ▲] Detailed reference viewed: 97 (11 ULg)Multiscale Quasistatic Homogenization for Laminated Ferromagnetic Cores Niyonzima, Innocent ; Vazquez Sabariego, Ruth ; Dular, Patrick et al in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC 2012) (2012, July 03) In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization method based on the heterogeneous multiscale method (HMM) with inclusion of a ... [more ▼] In this paper, we investigate the modeling of ferromagnetic multiscale materials. We propose a computational homogenization method based on the heterogeneous multiscale method (HMM) with inclusion of a hysteresis model. The HMM involves: 1) a macroscale problem that captures the slow variations of the overall solution; 2) many microscale problems that allow to determine the constitutive law at the macroscale. At the microscale, a novel energy consistent hystere- sis model is incorporated. As application example, a laminated iron core is considered. [less ▲] Detailed reference viewed: 112 (25 ULg)A dynamical model with hysteresis for the homogenization of ferromagnetic laminated cores ; Niyonzima, Innocent ; et al in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC2012) (2012, July) Detailed reference viewed: 67 (17 ULg)Finite Element Computational Homogenization of Nonlinear Multiscale Materials in Magnetostatics Niyonzima, Innocent ; V Sabariego, Ruth ; Dular, Patrick et al in IEEE Transactions on Magnetics (2012), 48(2), 587-590 The increasing use of composite materials in the technological industry (automotive, aerospace, ...) requires the development of effective models that account for the complexity of the microstructure of ... [more ▼] The increasing use of composite materials in the technological industry (automotive, aerospace, ...) requires the development of effective models that account for the complexity of the microstructure of these materials and the nonlinear behaviour they can exhibit. In this paper we develop a multiscale computational homogenization method for modelling nonlinear multiscale materials in magnetostatics based on the finite element method. The method solves the macroscale problem by getting data from certain microscale problems around some points of interest. The missing nonlinear constitutive law at the macroscale level is derived through an upscaling from the microscale solutions. The downscaling step consists in imposing a source term and determining proper boundary conditions for microscale problems from the macroscale solution. For a two-dimensional geometry, results are validated by comparison with those obtained with a classical brute force finite element approach and a classical homogenization technique. The method provides a good overall macroscale response and more accurate local data around points of interest. [less ▲] Detailed reference viewed: 135 (31 ULg)Finite Element Computational Homogenization for Heterogeneous Materials in Magnetodynamics Niyonzima, Innocent ; Vazquez Sabariego, Ruth ; Dular, Patrick et al in Proceedings of the Fifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) (2011, November) Detailed reference viewed: 41 (10 ULg)Finite Element Computational Homogenization of Nonlinear Multiscale Materials in Magnetostatics Niyonzima, Innocent ; V Sabariego, Ruth ; Dular, Patrick et al in 18th Conference on the Computation of Electromagnetic Fields (COMPUMAG2011) (2011) This paper deals with the modelling of nonlinear multiscale materials in magnetostatics by means of a finite element computational homogenization method. The method couples a macroscale problem with many ... [more ▼] This paper deals with the modelling of nonlinear multiscale materials in magnetostatics by means of a finite element computational homogenization method. The method couples a macroscale problem with many microscale problems. During the upscaling step, the homogenized magnetic permeability and its derivative with respect to the magnetic field are calculated from the microscale solution and transferred to the macroscale. The downscaling step consists in imposing proper boundary conditions for the microscale problems from the macroscale solution. Results are validated by comparison with those obtained with classical finite element brute force approach. [less ▲] Detailed reference viewed: 90 (18 ULg)A Xylophone Bar Magnetometer for micro/pico satellites ; Niyonzima, Innocent ; Rochus, Pierre et al in Acta Astronautica (2010), 67(7-8), 793-809 The Belgian Institute of Space Aeronomy (BIRA-IASB), "Centre Spatial de Liège" (CSL), "Laboratoire de Techniques Aéronautiques et Spatiales" (LTAS) of University of Liège, and the Microwave Laboratory of ... [more ▼] The Belgian Institute of Space Aeronomy (BIRA-IASB), "Centre Spatial de Liège" (CSL), "Laboratoire de Techniques Aéronautiques et Spatiales" (LTAS) of University of Liège, and the Microwave Laboratory of University of Louvain-La-Neuve (UCL) are collaborating in order to develop a miniature version of a xylophone bar magnetometer (XBM) using Microelectromechanical Systems (MEMS) technology. The device is based on a classical resonating xylophone bar. A sinusoidal current is supplied to the bar oscillating at the fundamental transverse resonant mode of the bar. When an external magnetic field is present, the resulting Lorentz force causes the bar to vibrate at its fundamental frequency with an amplitude directly proportional to the vertical component of the ambient magnetic field. In this paper we illustrate the working principles of the XBM and the challenges to reach the required sensitivity in space applications (measuring magnetic fields with an accuracy of approximately of 0.1 nT). The optimal dimensions of the MEMS XBM are discussed as well as the constraints on the current flowing through the bar. Analytical calculations as well as simulations with finite element methods have been used. Prototypes have been built in the Microwave Laboratory using Silicon on Insulator (SOI) and bulk micromachining processes. Several methods to accurately measure the displacement of the bar are proposed. [less ▲] Detailed reference viewed: 136 (28 ULg) |
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