Electrodynamics of Continua I: Foundations and Solid Media

ISBN-13: 9781461279235 / Angielski / Miękka / 2011 / 436 str.

A. Cemal Eringen; Gerard A. Maugin

Opis

The electrodynamics of continua is a branch ofthe physical sciences concerned with the interaction of electromagnetic fields with deformable bodies. De formable bodies are considered to be continua endowed with continuous distributions of mass and charge. The theory of electromagnetic continua is concerned with the determination of deformations, motions, stress, and elec tromagnetic fields developed in bodies upon the applications of external loads. External loads may be of mechanical origin (e.g., forces, couples, constraints placed on the surface of the body, and initial and boundary conditions arising from thermal and other changes) and/or electromagnetic origin (e.g., electric, magnetic, and current fields). Because bodies of different constitutions respond to external stimuli in a different way, it is imperative to characterize properly the response functions relevant to a given class of continua. This is done by means of the constitutive theory. For example, an elastic dielectric responds to electromagnetic fields in a totally different way than a magnetic fluid. The present book is intended to present a unified approach to the subject matter, based on the principles of contemporary continuum physics."

Spis treści

(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.