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Table of contents
List of figures
Résumé en Français
General Introduction
1 Basic Equations for the Modeling of Soft Magnetic Composites
1.1 Maxwell’s Equations
1.2 Constitutive Relations
1.2.1 Magnetic Behavior
1.2.2 Mechanical Behavior
1.2.3 Magneto-Mechanical Behavior
1.3 Eddy Current Losses
1.3.1 EC Loss Density Definition
1.3.2 EC Loss Density of Homogeneous Structures
1.4 Soft Magnetic Composites
1.4.1 EC Loss Density of SMC
1.5 Homogenization Techniques
1.6 Conclusion
2 A Complex Permeability Model for EC Losses in SMC
2.1 EC Loss Density of Single Inclusion
2.1.1 Cylindrical Inclusion
2.1.2 Spherical Inclusion
2.2 EC Loss Density of SMC
2.3 Effective Permeability of SMC
2.3.1 MG Estimate
2.3.2 Series Expansion Estimate
2.4 Complex Permeability Definition
2.4.1 Complex Permeability of Single Inclusion
2.4.2 Complex Permeability of SMC
2.5 Validation using FEM computations
2.5.1 Microstructure
2.5.2 Parameters
2.5.3 Effective Permeability Comparison
2.5.4 EC Loss Density Comparison
2.5.5 EC Loss Density by Average Field Assumption
2.5.6 EC Loss Density by Effective Complex Permeability Tensor
2.6 Discussion
2.6.1 Square Microstructure
2.6.2 Cube Microstructure
2.6.3 Complex Permeability
2.7 Conclusion
3 Bounds and Estimates on EC Losses in SMC
3.1 EC Loss Density in SMC
3.2 Bounds
3.2.1 Cylinder Microstructure
3.2.2 Sphere Microstructure
3.2.3 Extension to More Generic Microstructures
3.3 EC Loss Density Estimates
3.3.1 Cylinder Microstructure
3.3.2 Sphere Microstructure
3.4 Discussion
3.4.1 Numerical Calculations on EC Losses Estimates
3.4.2 Model Validation
3.5 Conclusion
4 Complex Permeability for SMC: Application to Magnetic Circuit
4.1 EC Loss Density of High Concentration SMC
4.1.1 Perpendicular field
4.1.2 In-plane field
4.1.3 Complex permeability for SMC
4.2 Magnetic Circuit Application
4.2.1 Magnetic Behavior
4.2.2 EC Loss Density
4.3 Conclusion
5 Effect of Stress on Eddy Current Losses in Soft Magnetic Composites
5.1 Basic Constitutive Equations
5.1.1 EC Loss Density in a Cube-shaped Inclusion
5.1.2 Stress-dependent Magnetic Permeability
5.1.3 EC Losses In a Cube Subjected To Stress
5.2 Loss Density in SMC
5.2.1 Homogenization Technique
5.3 Model Prediction and Results
5.3.1 Material Parameters
5.3.2 Stress Effect
5.4 Conclusion
Conclusion and Perspectives
References
