Electrodynamics of Continua I: Foundations and Solid Media


This book presents a unified approach to the electrodynamics of continua, based on the principles of contemporary continuum of physics. This interdisciplinary approach is unique for the treatment of the subject matter, and much of the material is new or newly composed. No other treatise similar in content and composition to this one exists at this time. The authors present a self-contained, finite deformation and finte electro-magnetic field theory from a unified viewpoint, providing ample critical illustrations ...

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This book presents a unified approach to the electrodynamics of continua, based on the principles of contemporary continuum of physics. This interdisciplinary approach is unique for the treatment of the subject matter, and much of the material is new or newly composed. No other treatise similar in content and composition to this one exists at this time. The authors present a self-contained, finite deformation and finte electro-magnetic field theory from a unified viewpoint, providing ample critical illustrations by way of applications. The constitution of the book is as follows: (1) development of the ten basic balance laws in order to establish the macroscopic electromagnetic theory; (2) establishment of the general constitutive theory. By means of eight axioms, the local nonlinear theory is developed for finite deformations and E-M (electromagnetic) fields. In this way, for the first time, it has been possible to express the nonlinear constitutive equations for the ninety magnetic groups relevant to magnetic crystals. (3) discussion of special theories and applications. Various special topics are explored and solutions presented to several nonlinear problems in order to demonstrate the uses of the basic theory. The book is intended primarily as a guide and reference for researchers, although selected chapters can well be used as a textbook for graduate studies.

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Editorial Reviews

The interaction of electromagnetic fields with bulk matter is a topic of obviously high technological importance, but a topic made famously complicated by the fact that bulk matter can be "constituted" in so many radically diverse ways. In this major monograph the emphasis is on that aspect of the topic which relates to deformable matter (whether solid or fluid). The authors (both at Princeton when the project was conceived) have produced a 2-volume work which has the outward appearance of a graduate level textbook (exercises at the end of each of the 23 chapters), but which contains so much new material and is so uncompromisingly detailed that it will be of value mainly to their professional peers. Physical and mathematical fundamentals are in very clear focus. Very handsomely produced. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781461279235
  • Publisher: Springer New York
  • Publication date: 7/31/2012
  • Edition description: Softcover reprint of the original 1st ed. 1990
  • Edition number: 1
  • Pages: 436
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.96 (d)

Table of Contents

(Volume I).- 1 Kinematics of Material Continua.- 1.1. Scope of the Chapter.- 1.2. Mass and Charge.- 1.3. Motion and Deformation.- 1.4. Strain Measures.- 1.5. Polar Decomposition.- 1.6. Infinitesimal Strains.- 1.7. Volume and Area Changes.- 1.8. Compatibility Conditions.- 1.9. Deformation Rates.- 1.10. Rigid Body Motion.- 1.11. Objectivity.- 1.12. Objective Time Rates of Tensor Fields.- 1.13. Kinematics of Line, Surface, and Volume Integrals.- Problems.- 2 Microscopic Electromagnetic Theory.- 2.1. Scope of the Chapter.- 2.2. Electric Charge.- 2.3. Electric Moments.- 2.4. Current, Magnetic Moments.- 2.5. Microscopic Electromagnetic Fields.- 2.6. Electromagnetic Force on a Point Particle.- 2.7. Microscopic Maxwell’s Equations.- 2.8. Electromagnetic Force on Composite Particles.- 2.9. Couple Acting on a Composite Particle.- 2.10. Power of Electromagnetic Forces.- Problems.- 3 Macroscopic Electromagnetic Theory.- 3.1. Scope of the Chapter.- 3.2. Statistical Averages.- 3.3. Maxwell’s Equations.- 3.4. Galilean Invariance of Maxwell’s Equations.- 3.5. Macroscopic Densities of Mass, Force, Couple, and Power.- A. Mass Density.- B. Force Density.- C. Couple Density.- D. Electromagnetic Power.- 3.6. Electromagnetic Stress Tensor, Momentum, and Poynting Vector.- 3.7. Electromagnetic Force, Couple, and Power at a Discontinuity Surface.- 3.8. Balance Laws of Continuum Physics.- 3.9. Balance Laws of Electrodynamics.- A. Global Statement.- B. Local Balance Laws.- C. Boundary Conditions.- 3.10. Thermomechanical Balance Laws.- 3.11. Clausius-Duhem Inequality.- 3.12. Invariance Requirements for Balance Laws.- 3.13. Principle of Virtual Power.- 3.14. Résumé of Balance Laws.- Problems.- 4 Elementary Properties of Electromagnetic Continua.- 4.1. Scope of the Chapter.- 4.2. Dielectric Materials.- 4.3. Physical Theory of Dielectrics.- A. Polarizability.- B. The Clausius-Mossoti Equation.- C. Ferroelectric Crystals.- D. Electrostriction and Piezoelectricity.- E. Pyroelectricity.- 4.4. Magnetic Materials.- A. The Origin of Magnetism.- B. Gyromagnetic Effects.- 4.5. Different Types of Magnetism.- A. Paramagnetism.- B. Ferromagnetism.- C. Ferrimagnetism and Antiferromagnetism.- D. Magnons.- E. Magnetostriction and Piezomagnetism.- 4.6. Electric Conduction.- A. Electron Conduction.- B. Cross Effects.- 4.7. Interaction Between Light and Electromagnetic Continua.- A. Electromagnetic Optics.- B. Inducement of Optical Anisotropy.- Problems.- 5 Constitutive Equations.- 5.1. Scope of the Chapter.- 5.2. Résumé of Balance Laws.- 5.3. Raison d’Être.- 5.4. Axioms of Constitutive Theory.- A. Axiom of Causality.- B. Axiom of Determinism.- C. Axiom of Equipresence.- D. Axiom of Objectivity.- E. Axiom of Time Reversal.- F. Axiom of Material Invariance.- G. Axiom of Neighborhood.- H. Axiom of Memory.- I. Axiom of Admissibility.- 5.5. Integrity Basis Under Crystallographic Point Groups.- 5.6. Integrity Basis Under Magnetic Point Groups.- 5.7. Integrity Basis of Vectors and Tensors for Isotropic Materials.- 5.8. Constitutive Equations of Electromagnetic Elastic Solids.- 5.9. Isotropic Electromagnetic Elastic Solids.- 5.10. Anisotropic Electromagnetic Elastic Solids.- 5.11. Linear Constitutive Equations.- 5.12. Electromagnetic Fluids.- 5.13. Résumé of Constitutive Equations.- Problems.- 6 Rigid Dielectrics.- 6.1. Scope of the Chapter.- 6.2. Fundamental Equations.- 6.3. Potential Theory.- A. Green’s Theorem.- B. Uniqueness Theorem.- C. Representation Theorem.- D. Green’s Function.- E. Green’s Function for Dirichlet’s Problem in Spherical Regions and in Half-Space.- F. Eigenfunction Expansions.- 6.4. Charged Cylinder.- 6.5. Potential in Half-Plane.- 6.6. Charged Disk.- 6.7. Plane Electromagnetic Waves in Isotropic Bodies.- 6.8. Spherical Waves.- 6.9. Nonlinear Theory of Rigid Dielectrics.- 6.10. One-Dimensional Problem.- 6.11. Two-Dimensional Nonlinear Problem.- 6.12. Solutions of Two-Dimensional Problems for Special Dielectrics.- 6.13. Nonlinear Electromagnetic Waves.- 6.14. Electromagnetic Shock Waves in Rigid Stationary Dielectrics.- 6.15. Moving Rigid Dielectrics.- A. Dragging of Light by a Moving Dielectric.- B. The Rotation of a Rigid Dielectric in a Magnetic Field.- C. Unipolar Induction.- 6.16. Nonlinear Optics.- 6.17. Solitary Waves.- Problems.- 7 Elastic Dielectrics.- 7.1. Scope of the Chapter.- 7.2. Résumé of Basic Equations..- 7.3. Uniqueness Theorem.- 7.4. Piezoelectric Moduli.- 7.5. Piezoelectrically Excited Thickness Vibrations of Plates.- 7.6. Extensional Vibrations of Piezoelectric Rods.- 7.7. Surface Waves.- 7.8. Radially Symmetric Vibrations.- 7.9. Spherically Symmetric Vibrations of Thin Ceramic Shells.- 7.10. Piezoelectrically Generated Electric Field.- 7.11. Elastic Dielectrics Subject to Finite Deformations and Fields.- 7.12. Cylindrically Symmetric Deformation of a Tube Subject to a Radial Field.- 7.13. Axisymmetric Oscillations of a Tube.- 7.14. Small Deformations and Fields Superimposed on Large Static Deformations and Fields.- 7.15. Photoelastic Effect.- 7.16. Electro-Optical Effect.- 7.17. Magneto-Optical Effects.- 7.18. Elastic Ionic Crystals, Ferroelectrics, and Other Polarizable Solids.- Problems.- 8 Magnetoelasticity.- 8.1. Scope of the Chapter.- 8.2. Résumé of Basic Equations.- 8.3. Static Magnetoelastic Fields.- 8.4. Uniformly Magnetized Sphere in Nonpermeable Medium.- 8.5. Two-Dimensional Magnetoelasticity.- 8.6. Stress Concentration at a Circular Hole.- 8.7. Radial Motions of a Cylinder Under an Axial Magnetic Field.- 8.8. Propagation of Plane Waves.- 8.9. Waves Induced by a Thermal Shock.- 8.10. Homogeneous Strain in a Magnet.- 8.11. Simple Shear.- 8.12. Torsion of a Cylindrical Magnet.- 8.13. Electric Conduction in a Twisted Cylinder.- 8.14. Theory of Magnetoelastic Plates.- 8.15. Plate under Transverse Magnetic Field.- 8.16. Magnetoelastic Buckling of a Circular Plate.- 8.17. Other Works: Dynamic Buckling and Nonlinear Waves.- Problems.- Appendices.- A. Crystallographic Point Groups.- B. Crystallographic Magnetic Groups.- C. Integrity Bases of Crystallographic Groups.- D. Some Theorems on Symmetric Polynomial Functions.- E. Representations of Isotropic, Scalar, Vector, and Tensor Functions.- F. Maxwell’s Equations in Various Systems of Units.- References.

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