A. Aharoni, Theoretical Search for Domain Nucleation, Reviews of Modern Physics, vol.34, issue.2, pp.227-238, 1962.
DOI : 10.1103/RevModPhys.34.227

. [. Alpert, Adaptative solution of partial differential equations in multiwavelet bases, 2004.

Y. O. Amor and M. Féliachi, Finite Element Computation of iron losses in hysteresis ferromagnetic materials taking into account frequency and thermal effects, conférence Compumag 13ème, 2001.

B. [. Argyle, D. A. Petek, and . Herman, Optical imaging of magnetic domains in motion (invited), Journal of Applied Physics, vol.61, issue.8, pp.4303-4306, 1987.
DOI : 10.1063/1.338453

M. V. Chari and S. J. Salon, Numerical methods in Electromagnetism, 2000.

N. [. Ashcroft and . Mermin, Physique des solides, E.D.P. Sciences, 2002.

. Atherton, Magnetic Barkhausen noïse study of domain wall dynamics in 3% SiFe, IEEE Transactions on Magnetics, vol.32, pp.527-534, 1996.

M. Attéia and J. Gaches, Approximation hilbertienne: Splines- Ondelettes-fractales, E.D.P. Sciences, 2002.

G. Auliac, J. Avignant, and E. Azoulay, Techniques mathématiques pour la physique, 2000.

C. Henaux, Enjeu des mat??riaux magn??tiques composites pour les machines ??lectriques du futur, Revue de l'Electricit?? et de l'Electronique, vol.-, issue.08, pp.29-33, 2003.
DOI : 10.3845/ree.2003.093

. [. Benabou, Contribution à la caractérisation et à la modélisation de matériaux magnétiques, INP Lilles, 2002.

[. Barbara, Magnetization processes in high anisotropy systems, Journal of Magnetism and Magnetic Materials, vol.129, issue.1, pp.79-86, 1994.
DOI : 10.1016/0304-8853(94)90432-4

S. [. Bean, Kinetics of Magnetization in Some Square Loop Magnetic Tapes, Journal of Applied Physics, vol.26, issue.1, pp.124-125, 1955.
DOI : 10.1063/1.1721848

C. [. Rodbell and . Bean, Some Properties of the Coercive Force in Soft Magnetic Materials, Physical Review, vol.103, issue.4, pp.886-891, 1956.
DOI : 10.1103/PhysRev.103.886

C. [. Pry and . Bean, Calculation of the Energy Loss in Magnetic Sheet Materials Using a Domain Model, Journal of Applied Physics, vol.29, issue.3, pp.532-533, 1958.
DOI : 10.1063/1.1723212

J. J. Becker, Domain Boundary Configurations during Magnetization Reversals, Journal of Applied Physics, vol.30, issue.3, pp.387-390, 1959.
DOI : 10.1063/1.1735173

. [. Bergqvist, A simple vector generalization of the Jiles-Atherton model of hysteresis, IEEE Transactions on Magnetics, vol.32, issue.5, pp.4213-4215, 1996.
DOI : 10.1109/20.539337

A. [. Bergqvist and G. Lundgren, Experimental testing of an anisotropic vector hysteresis model, IEEE Transactions on Magnetics, vol.33, issue.5, pp.4152-4154, 1997.
DOI : 10.1109/20.619693

. [. Bernard, Contribution à la modélisation des systèmes électromagnétiques en tenant compte du phénomène d'hystérésis, 2000.

E. [. Bernard, F. Mendes, and . Bouillault, Dynamic hysteresis modeling based on Preisach's model, conférence Compumag 13ème, 2001.

G. Bertotti, Dynamics of microscopic magnetization processes and magnetic losses (invited), Journal of Applied Physics, vol.53, issue.11, pp.8287-8292, 1982.
DOI : 10.1063/1.330344

. [. Bertotti, Space???time correlation properties of the magnetization process and eddy current losses: Theory, Journal of Applied Physics, vol.54, issue.9, pp.5293-5305, 1983.
DOI : 10.1063/1.332705

F. [. Bertotti and . Fiorillo, Power losses and domain structure dynamics in 3% SiFe single crystals, IEEE Transactions on Magnetics, vol.20, issue.5, pp.1475-1477, 1984.
DOI : 10.1109/TMAG.1984.1063486

. [. Bertotti, Space???time correlation properties of the magnetization process and eddy current losses: Applications. I. Fine wall spacing, Journal of Applied Physics, vol.55, issue.12, pp.4339-4347, 1984.
DOI : 10.1063/1.333001

. [. Bertotti, Space???time correlation properties of the magnetization process and eddy current losses: Applications. II. Large wall spacing, Journal of Applied Physics, vol.55, issue.12, pp.4348-4355, 1984.
DOI : 10.1063/1.333002

. [. Bertotti, A general statistical approach to the problem of eddy current losses, Journal of Magnetism and Magnetic Materials, vol.41, issue.1-3, pp.253-260, 1984.
DOI : 10.1016/0304-8853(84)90192-6

. [. Bertotti, Physical interpretation of eddy current losses in ferromagnetic materials. I. Theoretical considerations, Journal of Applied Physics, vol.57, issue.6, pp.2110-2117, 1985.
DOI : 10.1063/1.334404

. [. Bertotti, Physical interpretation of eddy current losses in ferromagnetic materials. II. Analysis of experimental results, Journal of Applied Physics, vol.57, issue.6, pp.2118-2126, 1985.
DOI : 10.1063/1.334405

. [. Bertotti, General properties of power losses in soft ferromagnetic materials, IEEE Transactions on Magnetics, vol.24, issue.1, pp.621-630, 1988.
DOI : 10.1109/20.43994

V. [. Bertotti, M. Basso, and . Pasquale, Application of the Preisach model to the calculation of magnetization curves and power losses in ferromagnetic materials, IEEE Transactions on Magnetics, vol.30, issue.2, 1993.
DOI : 10.1109/20.312492

. [. Bertotti, Hysteresis in magnetism, 1998.

P. Bertrand, Les protections directionnelles Schneider- Electric, Cahier Technique n ? 181, pp.1-20, 1996.

O. Biro, Computation of 3-D current driven skin effect problems using a current vector potential, IEEE Transactions on Magnetics, vol.29, issue.2, pp.1325-1332, 1993.
DOI : 10.1109/20.250642

O. [. Hollaus and . Birò, Derivation of a complex permeability from the Preisach model, IEEE Transactions on Magnetics, vol.38, issue.2, pp.905-908, 2002.
DOI : 10.1109/20.996233

J. E. Bishop, Magnetic domain structure, eddy currents and permeability spectra, British Journal of Applied Physics, vol.17, issue.11, pp.1451-1459, 1966.
DOI : 10.1088/0508-3443/17/11/310

J. E. Bishop, Understanding magnetization losses in terms of eddy current dominated domain wall dynamics, Journal of Magnetism and Magnetic Materials, vol.19, issue.1-3, pp.336-344, 1980.
DOI : 10.1016/0304-8853(80)90626-5

. [. Bishop, Modelling domain wall motion in soft magnetic alloys, Journal of Magnetism and Magnetic Materials, vol.41, issue.1-3, pp.261-271, 1984.
DOI : 10.1016/0304-8853(84)90193-8

J. E. Bishop, Enhanced eddy current loss due to domain displacement, Journal of Magnetism and Magnetic Materials, vol.49, issue.3, pp.241-249, 1985.
DOI : 10.1016/0304-8853(85)90154-4

. [. Bitter, On Inhomogeneities in the Magnetization of Ferromagnetic Materials, Physical Review, vol.38, issue.10, pp.1903-1905, 1931.
DOI : 10.1103/PhysRev.38.1903

. [. Blache, Modélisation électronique et électromagnétique d'un transformateur Haute Fréquence à circuit magnétique en fonte, 1995.

O. Doblecker, Contribution à la modélisation des champs magnétiques dans les systèmes comportant des milieux non-linéaires et hystérétiques, 2001.

C. [. De-blois and . Graham, Domain Observations on Iron Whiskers, Journal of Applied Physics, vol.29, issue.3, pp.528-529, 1958.
DOI : 10.1063/1.1723210

. [. Bossavit, Le calcul des courants de Foucault en 3D en présence de corps à haute perméabilité magnétique, pp.1147-1159, 1988.

. [. Bossavit, Le calcul des courants de Foucault en 3D, avec le champ électrique E comme inconnue I: Principes " , Revue de Physique Appliquée, pp.189-197, 1990.
DOI : 10.1051/rphysap:01990002502018900
URL : https://hal.archives-ouvertes.fr/jpa-00246178/document

. [. Boudaud, Mathématiques pour la Physique, 1996.

. Brailsford, Physical principles of magnetism, 1966.

P. Brissonneau, Magnétisme et matériaux magnétiques, 1997.

W. F. Brown, Theory of the Approach to Magnetic Saturation, Physical Review, vol.58, issue.8, pp.736-743, 1940.
DOI : 10.1103/PhysRev.58.736

. [. Brown, The Effect of Dislocations on Magnetization Near Saturation, Physical Review, vol.60, issue.2, pp.139-147, 1941.
DOI : 10.1103/PhysRev.60.139

. [. Brown, Criterion for Uniform Micromagnetization, Physical Review, vol.105, issue.5, pp.1479-1482, 1957.
DOI : 10.1103/PhysRev.105.1479

W. F. Brown, Micromagnetics: Domain walls / Micromagnetics, Domains and resonance, Journal of Applied Physics, vol.30, issue.4, pp.625-695, 1959.
DOI : 10.1063/1.2185970

. [. Brown, Domains, micromagnetics, and beyond: Reminiscences and assessments, Journal of Applied Physics, vol.49, issue.3, pp.1937-1942, 1978.
DOI : 10.1063/1.324811

H. [. Bryant and . Suhl, Micromagnetics below saturation, Journal of Applied Physics, vol.66, issue.9, pp.4329-4337, 1989.
DOI : 10.1063/1.343980

. [. Calvas, Les dispositifs Différentiels résiduels en Basse Tension, 2001.

. [. Calvas, Perturbations électriques en basse tension, pp.1-27, 2001.

. [. Carr, Magnetic domain wall bowing in a perfect metallic crystal, Journal of Applied Physics, vol.47, issue.9, pp.4176-4181, 1976.
DOI : 10.1063/1.323283

. [. Carr, Wall bowing and stability, Journal of Applied Physics, vol.48, issue.12, p.5379, 1977.
DOI : 10.1063/1.323545

M. Chiampi, D. Chiarabaglio, and M. Repetto, A Jiles-Atherton and fixed-point combined technique for time periodic magnetic field problems with hysteresis, IEEE Transactions on Magnetics, vol.31, issue.6, pp.4306-4311, 1995.
DOI : 10.1109/20.488295

J. [. Chen and . Muñoz, Theoretical eddy-current permeability spectra of slabs with bar domains, IEEE Transactions on Magnetics, vol.33, issue.3, pp.2229-2244, 1997.
DOI : 10.1109/20.573838

. [. Chen, Controlling Chaos and Bifurcations in engineering Systems, 2000.

. [. Chikasumi, Physics of Ferromagnetism, 1997.

J. Cledière, Simulation de processus d'aimantation dans les matériaux à anisotropie aléatoire et propriétés dynamiques d'aimantation dans des rubans nanocristallins doux, 1999.

B. [. Cohen-tannoudji, F. Diu, and . Laloë, Mécanique quantique (tome 2) Hermann, éditeur des sciences et des arts Mécanique quantique (tome 1), 2000.

G. [. Coleman and . Scott, Magnetic Domain Patterns on Iron Whiskers, Journal of Applied Physics, vol.29, issue.3, pp.526-527, 1958.
DOI : 10.1063/1.1723209

. [. Couderchon, Alliages FeNi et FeCo: propriétés magnétiques, pp.1-24, 2003.

C. [. Croissant, M. K. Feickert, and . Mcinerney, A differential magnetic permeability model for pulsed magnetic field calculations, IEEE Transactions on Magnetics, vol.32, issue.5, pp.4326-4328, 1996.
DOI : 10.1109/20.538858

H. [. Cutler and . Angus, A theoretical analysis of initial permeability in 36???50% Ni-Fe alloys, Journal of Magnetism and Magnetic Materials, vol.19, issue.1-3, pp.211-214, 1980.
DOI : 10.1016/0304-8853(80)90594-6

. [. Darrigol, Les équations de Maxwell -de MacCullagh à Lorentz, 2005.

[. Broglie, Application des équations non-linéaires à la physique théorique, 1962.

. [. Del-vecchio, An efficient procedure for modeling complex hyseresis processes in ferromagnetic materials, IEEE Transactions on Magnetics, issue.5, pp.16-809, 1980.

. [. Del-vecchio, Computation of losses in nonoriented electrical steels from a classical viewpoint (invited), Journal of Applied Physics, vol.53, issue.11, pp.8281-8286, 1982.
DOI : 10.1063/1.330307

. [. Del-vecchio, Calculation of magnetic domain wall bowing and eddy current losses in an infinite sheet of bar???like domains, Journal of Applied Physics, vol.53, issue.3, pp.2777-2779, 1982.
DOI : 10.1063/1.330964

. [. Del-vecchio, The inclusion of hysteresis processes in a special class of electromagnetic finite element calculations, IEEE Transactions on Magnetics, vol.18, issue.1, pp.275-284, 1982.
DOI : 10.1109/TMAG.1982.1061779

. [. Dionne, Magnetic relaxation and anisotropy effects on high-frequency permeability, IEEE Transactions on Magnetics, vol.39, issue.5, pp.3121-3126, 2003.
DOI : 10.1109/TMAG.2003.816026

. [. Delincé, Modélisation de régimes transitoires dans les systèmes comportant des matériaux magnétiques non-linéaires et hystérétiques, Faculté des sciences appliquées de Lièges, 1994.

M. [. Dobrovitski, B. N. Katsnelson, and . Harman, Statistical coarse-graining as an approach to multiscale problems in magnetism, Journal of Magnetism and Magnetic Materials, vol.221, issue.3, pp.235-242, 2000.
DOI : 10.1016/S0304-8853(00)00492-3

. [. Ducharne, Caractérisation et modélisation de circuits magnétiques, 2003.

P. Dular, A 3-D magnetic vector potential formulation taking eddy currents in lamination stacks into account, IEEE Transactions on Magnetics, vol.39, issue.3, pp.1424-1427, 2001.
DOI : 10.1109/TMAG.2003.810386

C. [. Dular and . Geuzaine, Modeling of thin insulating layers with dual 3-D magnetodynamic formulations, IEEE Transactions on Magnetics, vol.39, issue.3, pp.1139-1142, 2003.
DOI : 10.1109/TMAG.2003.810387

J. Gyselinck and P. Dular, A Time-Domain Homogenization Technique for Laminated Iron Cores in 3-D Finite-Element Models, IEEE Transactions on Magnetics, vol.40, issue.2, pp.856-859, 2004.
DOI : 10.1109/TMAG.2004.825152

R. [. Dupré, J. Van-keer, and . Melkebeek, An iron loss model for electrical machines using the Preisach theory, IEEE Transactions on Magnetics, vol.33, issue.5, pp.4158-4160, 1997.
DOI : 10.1109/20.619695

J. [. Dupré, J. A. Gyselinck, and . Melkebeek, Complementary finite element methods in 2D magnetics taking into account a vector Preisach model, IEEE Transactions on Magnetics, vol.34, issue.5, pp.3048-3051, 1998.
DOI : 10.1109/20.717713

. [. Ekstein, Theory of Remagnetization of Thin Tapes, Journal of Applied Physics, vol.26, issue.11, pp.1342-1343, 1955.
DOI : 10.1063/1.1721905

M. Enokizono and K. Okamoto, Designing a low-loss induction motor considering the vector magnetic properties, conférence Compumag 13ème, 2001.
DOI : 10.1109/20.996226

M. Enokizono and Y. Fujita, Improvement of E&S modeling for eddy-current magnetic field analysis, conférence Compumag 13ème, 2001.
DOI : 10.1109/20.996227

. [. Fonti, Transformateurs de courant: comment les spécifier?, 2001.

. [. Fonti, Transformateurs de courant: erreurs de spécification et solutions Schneider-Electric, Cahier Technique n ? 195, pp.1-18, 2001.

. [. Fouassier, Modélisation électrique des composants magnétiques Haute Fréquence: Prise en compte de la température et caractérisation des ferrites, 1998.

H. Fraisse, Modeling of a non-linear conductive magnetic circuit. 2. Bond graph formulation, IEEE Transactions on Magnetics, vol.31, issue.6, pp.4068-4070, 1995.
DOI : 10.1109/20.489864

. [. Friedman, New formulation of the Stoner???Wohlfarth hysteresis model and the identification problem, Journal of Applied Physics, vol.67, issue.9, pp.5361-5363, 1990.
DOI : 10.1063/1.344611

O. [. Fratila and J. L. Geoffroy, Propriétés dynamiques de l'aimantation dans les FeSi Goss, 2000.
DOI : 10.3166/rige.5.311-323

. [. Fratila, Etude de la multiplication des parois et estimation de l'anisotropie effective des nanocristallins, 2002.

O. Fruchart, Nanomagnétisme: des domaines confinés au magnétisme moléculaire, Bulletin de la SFP, vol.139, pp.11-17, 2003.

T. [. Fujiwara, N. Adachi, and . Takahashi, A proposal of Finite Element Analysis considering 2D magnetic properties, conférence Compumag 13ème, 2001.

J. K. Galt, J. Andrus, and H. G. Hopper, Motion of Domain Walls in Ferrite Crystals, Reviews of Modern Physics, vol.25, issue.1, pp.93-97, 1953.
DOI : 10.1103/RevModPhys.25.93

. [. Ganz, Applications of Thin Permalloy Tape in Wide-Band Telephone and Pulse Transformers, Transactions of the American Institute of Electrical Engineers, vol.65, issue.4, pp.46-73, 1946.
DOI : 10.1109/T-AIEE.1946.5059326

. [. Degauque, Materiaux magnétiques amorphes, micro et nanocristallins, pp.1-15, 2003.

. [. Gautreau, Modelisation d'un Capteur de courant basé sur un modèle de paroi, 2001.

. [. Geoffroy, Contribution à l'étude de l'irréversibilité dans les matériaux doux, Thèse de Doctorat / Physique -Sciences des matériaux, 1991.

O. Geoffroy, Matériaux magnétiques doux de l'Electrotechnique et applications, 2003.

. [. Giannacopoulos, Optimal Discretization-Based Load Balancing for Parallel Adaptive Finite-Element Electromagnetic Analysis, IEEE Transactions on Magnetics, vol.40, issue.2, pp.977-980, 2004.
DOI : 10.1109/TMAG.2004.824713

B. [. Gignoux and . Silvestre-brac, Mécanique: de la formulation Lagrangienne au Chaos Hamiltonien, E.D.P. Sciences, 2002.

. [. Gilbert, A Lagrangian of the gyromagnetic equation of the magnetization field, Physical Review, vol.100, p.1243, 1955.

. [. Gilbert, Classics in Magnetics A Phenomenological Theory of Damping in Ferromagnetic Materials, IEEE Transactions on Magnetics, vol.40, issue.6, pp.3443-3449, 2004.
DOI : 10.1109/TMAG.2004.836740

J. B. Goodenough, A Theory of Domain Creation and Coercive Force in Polycrystalline Ferromagnetics, Physical Review, vol.95, issue.4, pp.917-932, 1954.
DOI : 10.1103/PhysRev.95.917

J. Gyselinck, L. Vandevelde, and J. Melkebeek, Calculation of eddy currents and associated losses in electrical steel laminations, IEEE Transactions on Magnetics, vol.35, issue.3, pp.1191-1194, 1999.
DOI : 10.1109/20.767162

J. [. Haller and . Kramer, Observation of dynamic domain size variations in Si-Fe alloys, Journal of Applied Physics, issue.3, pp.41-1034, 1970.

J. [. Haller and . Kramer, Model for Reverse???Domain Nucleation in Ferromagnetic Conductors, Journal of Applied Physics, vol.41, issue.3, pp.1036-1037, 1970.
DOI : 10.1063/1.1658805

A. [. Haratani, I. Kaizu, and . Sato, Micromagnetic modeling of discrete patterned perpendicular media, IEEE Transactions on Magnetics, vol.39, issue.5, pp.2326-2328, 2003.
DOI : 10.1109/TMAG.2003.816286

W. [. Henze and . Rucker, Identification procedures of Preisach model, conférence Compumag 13ème, 2001.
DOI : 10.1109/20.996215

[. Chevalier, modélisation des pertes fer dans les machines électriques/ Application à la machine asynchrone, 1999.

[. Chevalier, A new dynamic hysteresis model for electrical steel sheet, Physica B: Condensed Matter, vol.275, issue.1-3, pp.197-201, 2000.
DOI : 10.1016/S0921-4526(99)00768-1

O. [. Hill, R. D. Farle, and . Edlinger, Finite Element Basis Functions for Nested Meshes of Nonuniform Refinement Level, IEEE Transactions on Magnetics, vol.40, issue.2, pp.981-984, 2004.
DOI : 10.1109/TMAG.2004.825149

M. Hintermüller and L. N. Vicente, Space Mapping for Optimal Control of Partial Differential Equations, SIAM Journal on Optimization, vol.15, issue.4, 2004.
DOI : 10.1137/S105262340342907X

L. Hirsinger, C. Lexcellent-dans, and R. E. , Alliages à mémoire de forme ferromagnétiques du type Ni-Mn-Ga -nouveaux matériaux actifs, pp.51-54, 2003.

H. [. Hitzinger and . Kronmüller, Statistical theory of the pinning of Bloch walls by randomly distributed defects, Journal of Magnetism and Magnetic Materials, issue.2, pp.11-17, 1976.

J. Hladik and P. E. Hladik, Le calcul tensoriel en physique, pp.Du- nod, 1999.

H. [. Hong, H. K. Kim, and . Jung, Formulation of the Everett function using least square method, IEEE Transactions on Magnetics, vol.34, issue.5, pp.3052-3055, 1998.
DOI : 10.1109/20.717714

. A. Hub_1, R. Hubert, and . Schafer, Magnetic domains, 2000.

K. [. Huyashi, Y. Saito, and . Nakatani, Calculation of Demagnetizing Field Distribution Based on Fast Fourier Transform of Convolution, Japanese Journal of Applied Physics, vol.35, issue.Part 1, No. 12A, pp.6065-6073, 1996.
DOI : 10.1143/JJAP.35.6065

S. A. Imphy and T. Lavoisier, Les alliages de Fer et de Nickel, Ed. Sc. G. Beranger, F. Duffaut, J. Morlet, J.F. Tiers, 1896.

D. [. Jiles and . Atherton, Theory of ferromagnetic hysteresis, Journal of Magnetism and Magnetic Materials, vol.61, issue.1-2, pp.48-60, 1986.
DOI : 10.1016/0304-8853(86)90066-1

. [. Jiles, Introduction to Magnetism and Magnetic Materials, 1991.
DOI : 10.1007/978-1-4615-3868-4

L. [. Jiles, G. Sipahi, and . Williams, Modeling of micromagnetic Barkhausen activity using a stochastic process extension to the theory of hysteresis, Journal of Applied Physics, vol.73, issue.10, pp.5830-5832, 1993.
DOI : 10.1063/1.353541

J. Coulomb, Le langage HE, Note interne au LEG, version 2.2 de novembre, 2000.

J. Gonnet, Optimisation des canalisations électriques et des armoires de distribution, 2005.

M. Kaltenbacher and S. Reitzingen, Algebraïc multigrid methods for nodal and edge based discretization of Maxwell Equations, ICS Newsletter, pp.15-23, 2003.

T. [. Kantartzis and . Tsiboukis, Higher order non-standard FDTD schemes in generalized curvilinear coordinates_A systematic strategy for advanced numerical modeling and consistent topological perpectives, ICS Newsletter, pp.5-14, 2003.

. [. Kedous-lebouc, A new hysteresis loop for rotational losses, Journal of Magnetism and Magnetic Materials, vol.160, pp.45-46, 1996.
DOI : 10.1016/0304-8853(96)00104-7

. [. Kittel, Ferromagnetic Domain Theory, Solid State Physics, pp.437-565, 1956.
DOI : 10.1016/S0081-1947(08)60136-8

D. [. Koehler and . Fredkin, Finite element methods for micromagnetics, IEEE Transactions on Magnetics, vol.28, issue.2, pp.1239-1244, 1992.
DOI : 10.1109/20.123912

. [. Koltermann, Non-linear magnetic field model by Finite Element Method taking into account hysteresis characteristics with MB variables, conférence Compumag 13ème, 2001.

. [. Krähenbühl, Homogenization of Lamination Stacks in Linear Magnetodynamics, IEEE Transactions on Magnetics, vol.40, issue.2, pp.912-915, 2004.
DOI : 10.1109/TMAG.2004.825435

. [. Kurz, A novel formulation for 3D eddy current problems with moving bodies using a Lagrangian description and BEM-FEM coupling, IEEE Transactions on Magnetics, vol.34, issue.5, 1998.
DOI : 10.1109/20.717718

. [. Friedlaender, Flux reversal in magnetic amplifier cores, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, vol.75, issue.3, pp.268-278, 1956.
DOI : 10.1109/TCE.1956.6372527

E. [. Landau and . Lifshitz, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies, pp.153-169, 1935.
DOI : 10.1016/B978-0-08-036364-6.50008-9

E. [. Landau, L. D. Lifchitz, E. M. Landau, and . Lifchitz, Electrodynamique des milieux continus, 1984.

. [. Laverrière, Electrodynamique Classique II / Electromagnétisme, 1992.

. [. Lebourgeois, Ferrites faibles pertes pour applications fréquentielles, pp.1-20, 2003.

. [. Leconte, Le mouvement dans la modélisation des phénomènes électromagnétiques (Chap. 2) " , dans " Electromagnétisme et Eléments Finis III, 2002.

D. Lederer and A. Kost, Modelling of non-linear magnetic materials using a complex effective reluctivity, IEEE Transactions on Magnetics, vol.34, issue.5, pp.3061-3063, 1998.

. [. Lefloch, Développement de formultions 3D FEM T-Phi pour la prise en compte de conducteurs massifs et bobinés avec couplage circuit, 2002.

Y. Lefloch, Coupled problem computation of 3-D multiply connected magnetic circuits and electric circuits, IEEE Transactions on Magnetics, vol.39, issue.3, pp.1725-1728, 2003.
DOI : 10.1109/TMAG.2003.810512

F. [. Leliakov and . Friedlaender, An improved model for flux reversal in Ni-Fe cores, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics, vol.80, issue.1, pp.23-26, 1961.
DOI : 10.1109/TCE.1961.6373067

M. Leroy, Contribution à la conception et l'optimisation d'architectures d'actionneurs, 2003.

. [. Lignelet, Fortran 77, Langage fortran V, 1985.

D. Lin, A Dynamic Core Loss Model for Soft Ferromagnetic and Power Ferrite Materials in Transient Finite Element Analysis, IEEE Transactions on Magnetics, vol.40, issue.2, pp.1318-1321, 2004.
DOI : 10.1109/TMAG.2004.825025

. [. Lochak, La géométrisation de la Physique, 1994.

B. Dupeloux, Modélisation des actionneurs électromagnétiques par réseaux de reluctances. Création d'un outil métier dédié au prédimensionnement par optimisation, 2006.

. [. Martin, Surface Structures and Ferromagnetic Domain Sizes, Proc. Phys. Soc, pp.77-84, 1956.
DOI : 10.1088/0370-1301/70/1/311

J. [. Marthouret, H. Masson, and . Fraisse, Modeling of a non-linear conductive magnetic circuit. 1. Definition and experimental validation of an equivalent problem, IEEE Transactions on Magnetics, vol.31, issue.6, pp.4065-4067, 1995.
DOI : 10.1109/20.489863

M. A. Raulet, J. P. Masson, and D. Gaude, Introduction d'une repr??sentation dynamique de mat??riau dans l'??quation de diffusion du champ magn??tique, The European Physical Journal Applied Physics, vol.1, issue.1, pp.73-76, 1998.
DOI : 10.1051/epjap:1998119

G. [. Mayergoyz and . Friedman, Isotropic vector Preisach model of hysteresis, Journal of Applied Physics, vol.61, issue.8, pp.4022-4024, 1987.
DOI : 10.1063/1.338565

G. [. Mayergoyz and . Friedman, Generalized Preisach model of hysteresis, IEEE Transactions on Magnetics, vol.24, issue.1, pp.212-217, 1988.
DOI : 10.1109/20.43892

A. [. Mayergoyz, G. Adly, and . Friedman, New Preisach???type models of hysteresis and their experimental testing, Journal of Applied Physics, vol.67, issue.9, pp.5373-5375, 1990.
DOI : 10.1063/1.346061

. [. Mayergoyz, Mathematical Models of hysteresis, 1991.

I. [. Adly and . Mayergoyz, Accurate modeling of vector hysteresis using a superposition of Preisach-type models, IEEE Transactions on Magnetics, vol.33, issue.5, pp.4155-4157, 1997.
DOI : 10.1109/20.619694

. [. Mayergoyz, Non-linear diffusion of electromagnetic fields, 1998.

V. Mazauric, Numerical modeling of electrical machines: requirements, state of the art, lacks, Journal of Magnetism and Magnetic Materials, vol.242, issue.245, pp.242-245, 2001.
DOI : 10.1016/S0304-8853(01)01299-9

. [. Mazauric, Champs et équations en électromagnétisme (chap. 2) " , dans " Electromagnétisme et Eléments Finis I: Formulations en Electromagnétisme, 2002.

V. Mazauric, From Thermostatistics to Maxwell's Equations: A Variational Approach of Electromagnetism, IEEE Transactions on Magnetics, vol.40, issue.2, pp.945-948, 2004.
DOI : 10.1109/TMAG.2004.825419

. [. Mazauric, An energy-based model for dynamic hysteresis, IEEE Transactions on Magnetics, vol.41, issue.10, 2005.
DOI : 10.1109/TMAG.2005.854877

C. [. Maraner, P. Beatrice, and . Mazzetti, Single Bloch wall dynamics in amorphous ribbons: A comparison between experimental and theoretical results, Journal of Applied Physics, vol.75, issue.8, pp.4117-4125, 1994.
DOI : 10.1063/1.355992

H. [. Meunier and Y. Luong, Computation of coupled problem of 3D eddy current and electrical circuit by using T/sub 0/-T-?? formulation, IEEE Transactions on Magnetics, vol.34, issue.5, pp.3074-3077, 1998.
DOI : 10.1109/20.717719

. [. Meunier, Couplage avec les équations de circuit (Chap. 1) " , dans " Electromagnétisme et Méthode des Eléments Finis III, 2002.

G. Meunier, Y. L. Floch, and C. Guérin, A nonlinear circuit coupled t - t/sub 0/ - ?? formulation for solid conductors, IEEE Transactions on Magnetics, vol.39, issue.3, pp.1729-1732, 2003.
DOI : 10.1109/TMAG.2003.810200

C. Mira, Systèmes asservis non-linéaires " . 1990: Hermès

. [. Néel, Les lois de l'aimantation et de la subdivision en domaines élémentaires d'un monocristal de Fer, Journal de Physique et le Radium, issue.11, pp.241-251, 1944.

. [. Néel, Quelques propriétés des parois magnétiques des domaines élémentaires ferromagnétiques, Cahier de Physique, pp.5-44, 1944.

. [. Néel, Influence de la subdivision en domaines élémentaires sur la perméabilité en haute fréquence des corps ferromagnétiques conducteurs " , annales de l'Institut Fourier, pp.301-319, 1951.

. [. Néel, Th??orie du tra??nage magn??tique de diffusion, Journal de Physique et le Radium, vol.13, issue.5, pp.249-264, 1952.
DOI : 10.1051/jphysrad:01952001305024900

. [. Nouredine, Modélisation de l'hystérésis dans les matériaux magnétiques et introduction de modèles dans Flux, 2002.

. [. Delannoy, Programmer en Fortran 90, guide complet, 2004.

V. [. Maloberti, G. Mazauric, A. Meunier, O. Kedous-lebouc, and . Geoffroy, An energy based formulation for dynamic hysteresis and extralosses, IEEE Transactions on Magnetics, conférence Compumag, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00189545

O. Maloberti, A. Kedous-lebouc, O. Geoffroy, G. Meunier, and V. Mazauric, Field diffusion-like representation and experimental identification of a dynamic magnetisation property, Journal of Magnetism and Magnetic Materials, 2005.

V. [. Maloberti, G. Mazauric, A. Meunier, O. Kedous-lebouc, Y. Geoffroy et al., A derivation of macroscopic Maxwell matter-field equations including dynamic magnetic hysteresis and extra-losses, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00184586

G. [. Maloberti, A. Meunier, V. Kedous-lebouc, O. Mazauric, and . Geoffroy, Vers une formulation de l'hyst??r??sis magn??tique dynamique vectorielle. Mod??lisation et identification exp??rimentale, Revue internationale de g??nie ??lectrique, vol.9, issue.4-5, 2005.
DOI : 10.3166/rige.9.515-529

V. [. Maloberti, G. Mazauric, A. Meunier, P. Kedous-lebouc, B. Wendling et al., A magnetic vector potential formulation to deal with dynamic hysteresis and induced losses within 2-D models, IEEE Transactions on Magnetics, conférence CEFC, 2006.

V. [. Maloberti, G. Mazauric, A. Meunier, and . Kedous-lebouc, A 3D electric vector potential formulation for dynamic hysteresis and losses, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.27, issue.1, 2006.
DOI : 10.1108/03321640810836834
URL : https://hal.archives-ouvertes.fr/hal-00365074

P. R. Gillette and K. Oshima, Magnetization Reversal by Rotation, Journal of Applied Physics, vol.29, issue.3, pp.529-531, 1958.
DOI : 10.1063/1.1723211

V. [. Ossart and . Ionita, Convergence de la m??thode du point fixe modifi??e ? pour le calcul de champ magn??tique avec hyst??r??sis, The European Physical Journal Applied Physics, vol.5, issue.1, pp.63-69, 1999.
DOI : 10.1051/epjap:1999105

O. [. Ossart, R. Hubert, and . Billardon, A new internal variables scalar hysteresis model exhibiting closed minor loops: Application to the prediction of the dynamic behaviour of electrical laminations, conférence Compumag 13ème, 2001.

. [. Ossart, Lois de comportement des matériaux (Chap. 2) " , dans " Electromagnétisme et Méthode des Eléments Finis II, 2002.

G. S. Park and S. Y. Kahn, Implementation of hysteresis characteristics using the Preisach model with M-B variables, IEEE Transactions on Magnetics, vol.29, issue.2, pp.1542-1545, 1993.
DOI : 10.1109/20.250697

J. B. Passioura, Simulation Models: Science, Snake Oil, Education, or Engineering?, Agronomy Journal, vol.88, issue.5, pp.690-694, 1996.
DOI : 10.2134/agronj1996.00021962008800050002x

E. [. Patel and . Della-torre, Fast computation of the CMH model, conférence Compumag 13ème, 2001.
DOI : 10.1109/20.996224

D. [. Friedberg and . Paul, New Theory of Coercive Force of Ferromagnetic Materials, Physical Review Letters, vol.34, issue.19, pp.1234-1237, 1975.
DOI : 10.1103/PhysRevLett.34.1234

. [. Peccolo, Frequency limits of a large signal dynamic model of magnetic circuits, Journal of Magnetism and Magnetic Materials, vol.160, pp.47-48, 1996.
DOI : 10.1016/0304-8853(96)00105-9

J. C. Perron, Matériaux ferromagnétiques amorphes et nanocristallins, pp.1-26, 2003.

R. [. Pfeifer and . Deller, Neue Werkstoffe für Impulsürbertrager, ETZ Elektrotechnische Zeitschrift Bd, vol.89, pp.601-603, 1968.

W. [. Pfeifer and . Behnke, Hohe Impulspermeabilität und hoher Induktionshub bei weichmagnetischen Ni-Fe-Werkstoffen mit kristallographischer Textur und magnetish induzierter Vorzugsrichtung, Z. Metallkde, issue.3, pp.70-142, 1979.

C. [. Pfeifer and . Radeloff, Soft magnetic Ni-Fe and Co-Fe alloys - some physical and metallurgical aspects, Journal of Magnetism and Magnetic Materials, vol.19, issue.1-3, pp.190-207, 1980.
DOI : 10.1016/0304-8853(80)90592-2

. [. Planck, Initiation à la Physique, 1941.

J. [. Vergne, J. C. Porteseil, and . Cotillard, From the motion of a Bloch wall to the magnetization of a polycrystal: Cooperative effects and scaling aspects, Journal of Magnetism and Magnetic Materials, vol.15, issue.18, pp.15-18, 1980.
DOI : 10.1016/0304-8853(80)90371-6

. [. Preisach, Über die magnetische Nachwirkung, Zeitschrift für Physik, p.94, 1935.

P. Nakmahachalasint, K. D. Ngo, and L. Vu-quoc, Thermal behavior of a dynamic domain-wall motion model for hysteresis in power ferrites, IEEE Transactions on Magnetics, vol.41, issue.1, pp.1-4, 2005.
DOI : 10.1109/TMAG.2004.839729

A. [. Brander and . Carey, The inverse scattering transformation method and the non-linear Schrödinger equation, pp.1-54, 1996.

. [. Raulet, Test of the sample geometry independance of a dynamic hysteresis behavioral model of magnetic materials, Journal of Magnetism and Magnetic Materials, pp.215-216, 2000.

M. A. Raulet, The Magnetic Field Diffusion equation Including Dynamic Hysteresis, IEEE Transactions on Magnetics, vol.42, issue.2, pp.872-875, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00141389

J. Reinert, A. Brockmeyer, and W. A. Donker, Calculation of losses in Ferro-and Ferrimagnetic materials based on the modified Steinmetz equation, IEEE Transactions on Magnetics, vol.37, issue.4, pp.1055-1060, 2001.

E. [. Reimers and . Della-torre, New Algorithm for implementing the specified vector Preisach model, conférence Compumag 13ème, 2001.

Z. Ren, T-?? formulation for eddy-current problems in multiply connected regions, IEEE Transactions on Magnetics, vol.38, issue.2, pp.557-560, 2002.
DOI : 10.1109/20.996146

[. Ribeiro, Teaching micromagnetism using computer demonstrations, conférence Compumag 13ème, 2001.

[. Bris, Systèmes multi-échelles -Modélisation et Simulation, Mathématiques et Applications n ? 47, 2005.

. [. Roters, Electromagnetic devices, 1941.

B. Roussin, Modélisation et optimisation d'un relais haute sensibilité -Mise en évidence des courants de Foucault, 1999.

G. Russakoff, A Derivation of the Macroscopic Maxwell Equations, American Journal of Physics, vol.38, issue.10, pp.38-1188, 1970.
DOI : 10.1119/1.1976000

D. [. Saliah, B. Lowther, and . Forghani, A neural network model of magnetic hysteresis for computational magnetics, IEEE Transactions on Magnetics, vol.33, issue.5, pp.3146-4148, 1997.

. Santi, Dynamic hysteresis in finemet thin films, IEEE Transactions on Magnetics, vol.39, issue.5, pp.2667-2668, 2003.

[. Savigny, Electroaimants de commande, Centrale Lyon, 1983.

J. Schneider, B. Springmann, and K. Zaveta, Magnetization reversal and domain boundary configurations in amorphous alloys, Journal of Magnetism and Magnetic Materials, vol.19, issue.1-3, pp.187-189, 1980.
DOI : 10.1016/0304-8853(80)90591-0

G. [. Shilling and . Houze, Magnetic properties and domain structure in grain-oriented 3% Si-Fe, IEEE Transactions on Magnetics, vol.10, issue.2, pp.195-222, 1974.
DOI : 10.1109/TMAG.1974.1058317

. [. Shimoji, A new modeling of the vector magnetic property, Compumag 13ème, 2001.
DOI : 10.1109/20.996222

[. S. Shur and Y. N. Dragoshanskiy, The shape of closure domains inside silicon-iron crystals, Fiz. Metal. Metalloved, vol.22, issue.5, pp.702-710, 1966.

S. Antonio-de, Energy Minimizers for large Ferromagnetic bodies, Arch. Rat. Mech. Anal, vol.125, pp.99-143, 1993.

. [. Slama, Modélisation 3D des effets d'induction, 2000.

J. C. Slonczewski, Dynamics of Magnetic domain walls, Intern. J. Magnetism, vol.2, pp.85-97, 1972.

J. C. Slonczewski, Theory of Bloch???line and Bloch???wall motion, Journal of Applied Physics, vol.45, issue.6, pp.2705-2715, 1974.
DOI : 10.1063/1.1663654

. [. Spornic, Frequency magnetic behaviour of SiFe sheets in a rotational field, Journal of Magnetism and Magnetic Materials, vol.160, pp.147-148, 1996.
DOI : 10.1016/0304-8853(96)00146-1

. [. Spornic, Automatisation de bancs de caractérisation 2D des tôles magnétiques -Influence des formes d'onde sur les mécanismes d'aimantation, 1998.

M. Brokate and J. Sprekels, Hysteresis and phase transitions, 1996.
DOI : 10.1007/978-1-4612-4048-8

E. [. Stoner and . Wohlfarth, A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.240, issue.826, pp.599-642, 1947.
DOI : 10.1098/rsta.1948.0007

J. Szczyglowski, Influence of eddy currents on magnetic hysteresis loops in soft magnetic materials, Journal of Magnetism and Magnetic Materials, vol.223, issue.1, pp.97-102, 2001.
DOI : 10.1016/S0304-8853(00)00584-9

J. Taylor, Incertitudes et analyse des erreurs dans les mesures physiques, 2000.

. [. Thiele, Steady-State Motion of Magnetic Domains, Physical Review Letters, vol.30, issue.6, pp.230-233, 1973.
DOI : 10.1103/PhysRevLett.30.230

. [. Thiele, Applications of the gyrocoupling vector and dissipation dyadic in the dynamics of magnetic domains, Journal of Applied Physics, vol.45, issue.1, pp.377-393, 1974.
DOI : 10.1063/1.1662989

. [. Tonti, On the mathematical structure of a large class of physical theories, Academia Nazionale Dei Lincei Serie VIII, vol.LII, issue.1, pp.48-56, 1972.

. [. Tonti, A mathematical model for physical theories, Serie VIII, pp.2-3, 1972.

. [. Tonti, The reason for analogies between physical theories, Applied Mathematical Modelling, vol.1, issue.1, pp.36-50, 1976.
DOI : 10.1016/0307-904X(76)90023-8

. [. Tonti, On the geometrical structure of electromagnetism, 1999.

G. Toulouse and M. Kléman, Principles of a classification of defects in ordered media, Journal de Physique Lettres, vol.37, issue.6, pp.149-151, 1976.
DOI : 10.1051/jphyslet:01976003706014900
URL : https://hal.archives-ouvertes.fr/jpa-00231261

D. Tremolet-de-lacheisserie, Magnétisme I: Fondements, Grenoble: E.D.P. Sciences, vol.I, 1999.

. Perrault, Optimisation d'un déclencheur à noyau plongeur, 1998.

. [. Ungemach, Temperature and field dependance of SiFe and CoPd single crystals, Journal of Magnetism and Magnetic Materials, pp.15-18, 1980.

E. [. Vajda and . Dellatorre, Characteristics of the complete moving hysteresis model, Journal of Applied Physics, vol.73, issue.10, pp.5833-5835, 1993.
DOI : 10.1063/1.353542

. [. Van-den, A. H. Berg, and . Brandt, Self???consistent domain theory in soft???ferromagnetic media. II. Basic domain structures in thin???film objects, Journal of Applied Physics, vol.60, issue.3, pp.1105-1113, 1986.
DOI : 10.1063/1.337352

. [. Van-den, A. H. Berg, and . Brandt, Self???consistent domain theory in soft???ferromagnetic media. III. Composite domain structures in thin???film objects, Journal of Applied Physics, vol.62, issue.5, pp.1952-1959, 1987.
DOI : 10.1063/1.339533

J. C. Bavay and J. Verdun, Alliages Fer-Silicium, 2003.

A. Viallix, A new method for finite element calculation of micromagnetic problems, IEEE Transactions on Magnetics, vol.24, issue.6, pp.2371-2373, 1988.
DOI : 10.1109/20.92112

. A. Vin_1, F. R. Salvini, and . Fulginei, Genetic algorithm and neural network generalizing the Jiles-Atherton model of static hysteresis for dynamic loops, conférence Compumag 13ème, 2001.

B. Vom-de-riet and F. Roozeboom, Ferromagnetic resonance and eddy currents in high-permeable thin films, Journal of Applied Physics, vol.81, issue.1, pp.350-354, 1997.
DOI : 10.1063/1.364118

P. [. Waeckerlé, D. Cremer, and R. E. Gautard-dans, Alliages magnétiques nanocristallins industriels -Etat de l'art, pp.22-28, 2003.

G. [. Wibbeler, W. Rassmann, and . Schatt, Nickel-Eisen-Kobalt- Magnetlegieringen mit stutenförmiger Hystereseschleife, Z. Metallkde Bd, vol.70, issue.1, pp.21-25, 1979.

D. [. Williams and . Dunlop, Three-dimensional micromagnetic modelling of ferromagnetic domain structure, Nature, vol.337, issue.6208, pp.634-637, 1989.
DOI : 10.1038/337634a0

R. [. Winter, G. G. Kuenning, and . Berg, Pulse properties of large 50-50 NiFe tape cores, IEEE Transactions on Magnetics, vol.6, issue.1, pp.41-45, 1970.
DOI : 10.1109/TMAG.1970.1066693

W. Wolf, Ein neuer weichmagnetischer Ni-Fe-Werkstoff f??r impuls??bertrager und drosseln in der leistungselektronik, Journal of Magnetism and Magnetic Materials, vol.9, issue.1-3, pp.170-172, 1978.
DOI : 10.1016/0304-8853(78)90045-8

J. [. Woodson and . Melcher, Electromechanical dynamic, 1968.

H. Williams, W. Shockley, and C. , Studies of the Propagation Velocity of a Ferromagnetic Domain Boundary, Physical Review, vol.80, issue.6, pp.1090-1094, 1950.
DOI : 10.1103/PhysRev.80.1090

K. [. Yamaguchi, T. Yamada, and . Takagi, Monte Carlo simulation for magnetic materials including dislocations, conférence Compumag 13ème, 2001.
DOI : 10.1109/20.996223

V. Zakharov, Application of inverse scatterin method to problems of differential geometry, pp.1-25, 2004.

. [. Zakharov, How classical physics helps mathematics, pp.1-24, 2004.

Z. [. Zàvèta, R. Kalva, and . Schäfer, Permeability and domain structure of a nanocrystalline alloy, Journal of Magnetism and Magnetic Materials, vol.148, issue.3, pp.390-396, 1995.
DOI : 10.1016/0304-8853(95)00056-9

J. [. Zegadi, B. Rousseau, and . Allard, Model of power soft MnZn ferrites, including temperature effects, IEEE Transactions on Magnetics, vol.36, issue.4, pp.2022-2032, 1995.
DOI : 10.1109/20.875308
URL : https://hal.archives-ouvertes.fr/hal-00140097

R. [. Couture and . Zitoun, Physique Statistique, p.Ellipses, 1992.

L. Matériaux-magnétiques-douxfe, . Ni, and . Co, énergie, guider les lignes de flux et transmettre des signaux Leur principale caractéristique est de s'aimanter aisément Ces matériaux sont aussi conducteurs et des courants sont induits en régime transitoire et périodique Ces derniers peuvent être classiquement diffusés à une échelle macroscopique mais aussi et surtout localement induits dans une microstructure magnétique en mouvement et réarrangement incessant Ces effets d'amortissement et de pertes dynamiques ont plusieurs conséquences parfois difficilement prévisibles: des pertes d'énergie, des temps de retard, de la distorsion de signal et de la rémanence. Nous nous intéressons à la recherche de modèles fidèles dans le but de comprendre les propriétés des matériaux ferromagnétiques doux en régime statique et dynamique et de simuler avec précision le comportement des dispositifs électrotechniques. Nous choisissons de nous concentrer particulièrement sur l'effet des courants induits microscopiques en plus de ceux macroscopiques, puisqu'ils sont à l'origine des pertes en excès et de l'hystérésis dynamique qui sont observées expérimentalement. Après avoir longuement étudié la problématique, les enjeux et les modèles existants; nous avons entrepris la construction d'une représentation des matériaux à l'échelle mésoscopique, les équations de champs dans la matière ont été redérivées en présence des processus physiques dynamiques mis en jeu

. Electromagnétisme-dans-la-matière, M. Modélisation, P. Magnétiques-doux, and . Fer, Hystérésis Dynamique, Caractérisations Expérimentales, Formulations Electromagnétiques, Simulations Numériques par la Méthode des Eléments Finis, Capteurs, Transformateurs de Courant, Actionneurs Electromécaniques, SOFT MAGNETIC MATERIALS: MEASUREMENTS AND SIMULATIONS

. Fe, . Ni, and . Co, to guide flux lines and to transmit information Their main characteristic is to be easilly magnetised They are also conducting and free currents are induced with time harmonics and transient signals These last can be classicaly diffused at the macroscopic scale but also and mainly locally induced in a moving microscopic magnetic structure. These damping effects and dynamic losses have got several consequences: power losses, time delay, signal distortion, remanence. We are interested in faithful models in order to understand soft materials static and dynamic properties and to compute power electrical devices with accuracy. We have chosen to focus on microscopic eddy currents in addition to macroscopic ones, because they are at the origin of the dynamic hysteresis which is observed and measured. After introducing the set of problems, stakes and state of the art; we began to build a theoretical material representation at the mesoscopic scale, between the microscopic and macroscopic ones, usable in material science and numerical simulation tools. So Matter- Field Equations have been derived again with the physics of dynamic magnetisation reversal processes. Then we tried to analyse the relevance and limits of our representation thanks to analytical calculations on simple and academic problems. We also carried out some calculations, measurements and experimental characterisations to confront theory and reality. Finally, we have written, with the Finite Element Method, some dedicated electromagnetic formulations in 3-D and 2-D. We have confirmed them with simple test cases always comparing with standard and previous results, analytical calculations and experimental observations, ABSTRACT Soft magnetic materials First simple configurations of circuit breaking applications have also been investigated, studied and computed. KEYWORDS Electromagnetism in Matter, Modeling, Soft Magnetic Materials, Iron Losses, Dynamic Hysteresis, Experimental Identification, Electromagnetic Formulations, Numerical Simulations