Electromagnetic field matter interactions in thermoelastic solids and viscous fluids

This book delivers a thorough derivation of nonrelativistic interaction models of electromagnetic field theories with thermoelastic solids and viscous fluids, the intention being to derive unique representations for the observable field quantities. This volume is intended for and will be useful to students and researchers working on all aspects of electromagneto-mechanical interactions in the materials sciences of complex solids and fluids.

1 General Introduction	p. 1
2 Basic Concepts	p. 7
2.1 Kinematics	p. 7
2.2 Equations of Balance	p. 9
2.2.1 The Balance Laws of Mechanics	p. 9
2.2.2 The Maxwell Equations	p. 11
2.2.3 Material Description	p. 14
2.3 The Entropy Production Inequality	p. 16
2.4 Jump Conditions	p. 18
2.5 Material Objectivity	p. 21
2.6 Constitutive Equations	p. 26
Part I Equivalence of Different Electromagnetic Formulations in Thermoelastic Solids
3 A Survey of Electromagneto-Mechanical Interaction Models	p. 33
3.1 Preview	p. 33
3.2 Scope of the Survey	p. 38
3.3 The Two-Dipole Models	p. 39
3.3.1 The Two-Dipole Model with a Nonsymmetric Stress Tensor (Model I)	p. 42
3.3.2 The Two-Dipole Model with a Symmetric Stress Tensor (Model II)	p. 51
3.4 The Maxwell-Minkowski Formulation (Model III)	p. 55
3.5 The Statistical Formulation (Model IV)	p. 66
3.6 The Lorentz Formulation (Model V)	p. 71
3.7 Thermostatic Equilibrium - Constitutive Equations	p. 77
3.8 Discussion	p. 83
4 Equivalence of the Models	p. 89
4.1 Preliminary Remarks	p. 89
4.2 Comparison of the Models I and II	p. 90
4.3 Comparison of the Models I and III	p. 91
4.4 Comparison of the Models III and IV	p. 93
4.5 Comparison of the Models IV and V	p. 96
4.6 Conclusions	p. 98
5 Material Description	p. 103
5.1 Motivation	p. 103
5.2 Material Description of the Two-Dipole Models (Models I and II)	p. 104
5.3 Material Description of the Statistical and the Lorentz Formulation	p. 117
5.4 Material Description of the Maxwell-Minkowski Formulation	p. 125
5.5 Thermostatic Equilibrium - Constitutive Relations for Energy Flux and Electric Current	p. 130
5.6 Recapitulation and Comparison	p. 132
5.7 Approach to a Unified Constitutive Theory	p. 138
6 Linearization	p. 147
6.1 Statement of the Problem	p. 147
6.2 Linearization of the Lorentz Model	p. 152
6.2.1 Motivation for this Choice - Governing Equations	p. 152
6.2.2 Decomposition of the Balance Laws	p. 156
6.2.3 Decomposition of the Constitutive Equations	p. 163
6.2.4 Decomposition of the Jump and Boundary Conditions	p. 169
6.3 Linearisation of the Other Models and Comparison	p. 170
6.4 The Meaning of Interchanging Dependent and Independent Constitutive Variables in one Formulation	p. 181
6.5 Discussion	p. 193
Part II Applications Magnetoelastic (In)stability and Vibrations Electrorheological Fluids
7 Magnetoelastic (In)stability and Vibrations	p. 201
7.1 Introduction	p. 201
7.2 Historical Review of Magnetoelastic Buckling Problems	p. 202
7.3 Ferromagnetic Systems	p. 205
7.3.1 Classical Method	p. 205
7.3.2 Variational Method for Ferromagnetic Systems	p. 210
7.3.3 Magnetoelastic Buckling of a Set of Two Soft Ferromagnetic Parallel Rods	p. 217
7.4 Superconducting Structures	p. 223
7.4.1 Formulation of Variational Principle for Superconducting Structures	p. 224
7.4.2 A Set of Two Concentric Superconducting Rings	p. 231
7.4.3 How to Use the Law of Biot and Savard in the Variational Principle	p. 235
7.5 Some Results for Superconducting Structures	p. 236
7.5.1 Review of Specific Structures and Some Results	p. 236
7.5.2 The Combined (Variational Biot-Savard) Method	p. 238
7.5.3 Helical or Spiral Superconductors	p. 245
7.5.4 Results	p. 252
7.6 Magnetoelastic Vibrations of Superconducting Structures	p. 256
7.6.1 Scope of this Section	p. 256
7.6.2 Magnetoelastic Vibrations of a Thin Soft Ferromagnetic Circular Plate in a Uniform Transverse Magnetic Field	p. 258
7.6.3 Magnetoelastic Vibrations of a Superconducting Ring in its Own Field	p. 271
7.6.4 Variational Principle for Magnetoelastic Vibrations of Superconducting Structures	p. 276
8 Electrorheological Fluids	p. 279
8.1 Introduction	p. 279
8.1.1 Overview	p. 282
8.2 Governing Equations and Constitutive Framework in Electrorheology	p. 283
8.2.1 The Electromagnetic Momentum Balance	p. 285
8.2.2 The Electromagnetic Energy Balance	p. 287
8.2.3 Non-relativistic Approximation	p. 287
8.2.4 The Total Balance Laws of Electrorheology	p. 293
8.2.5 Jump Conditions	p. 296
8.2.6 Discussion	p. 297
8.2.7 Constitutive Equations	p. 298
8.3 Constitutive Laws for the Cauchy Stress Tensor	p. 303
8.3.1 Models Proposed in the Literature	p. 303
8.3.2 Constitutive Laws Used in Our (Numerical) Approach	p. 311
8.4 Applications: Channel Flow of ERFs	p. 317
8.4.1 Formulation of the Problem - Electrodes Flush with the Channel	p. 318
8.4.2 Particular Case - Infinitely Long Electrodes	p. 322
8.4.3 Electrodes of Finite Length	p. 328
8.4.4 Electrodes with Modified Shape and Position Relative to the Flow - Experimental Results and Discussion	p. 361
9 Appendix	p. 367
9.1 Appendix A: On Objectivity	p. 367
9.2 Appendix B: Some Detailed Calculations of the Maxwell-Minkowski Model	p. 373
References	p. 375
Name Index	p. 391
Subject Index	p. 395

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