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Preface | p. ix |
Nonlinear Elasticity | p. 1 |
Preliminary Considerations | p. 1 |
The Equilibrium Problem | p. 2 |
Remarks About Equilibrium Boundary Problems | p. 4 |
Variational Formulation of Equilibrium | p. 7 |
Isotropic Elastic Materials | p. 11 |
Homogeneous Deformations | p. 12 |
Homothetic Deformation | p. 13 |
Simple Extension of a Rectangular Block | p. 16 |
Simple Shear of a Rectangular Block | p. 18 |
Universal Static Solutions | p. 21 |
Constitutive Equations in Nonlinear Elasticity | p. 24 |
Treolar's Experiments | p. 25 |
Rivlin and Saunders' Experiment | p. 26 |
Nondimensional Analysis of Equilibrium | p. 28 |
Signorini's Perturbation Method for Mixed Problems | p. 29 |
Signorini's Method for Traction Problems | p. 31 |
Loads with an Equilibrium Axis | p. 34 |
Second-Order Hyperelasticity | p. 36 |
A Simple Application of Signorini's Method | p. 38 |
Van Buren's Theorem | p. 40 |
An Extension of Signorini's Method to Live Loads | p. 45 |
Second-Order Singular Surfaces | p. 47 |
Singular Waves in Nonlinear Elasticity | p. 51 |
Principal Waves in Isotropic Compressible Elastic Materials | p. 53 |
A Perturbation Method for Waves in Compressible Media | p. 56 |
A Perturbation Method for Analyzing Ordinary Waves in Incompressible Media | p. 60 |
Micropolar Elasticity | p. 67 |
Preliminary Considerations | p. 67 |
Kinematics of a Micropolar Continuum | p. 68 |
Mechanical Balance Equations | p. 73 |
Energy and Entropy | p. 76 |
Elastic Micropolar Systems | p. 78 |
The Objectivity Principle | p. 81 |
Some Remarks on Boundary Value Problems | p. 86 |
Asymmetric Elasticity | p. 87 |
Continuous System with a Nonmaterial Interface | p. 91 |
Introduction | p. 91 |
Velocity of a Moving Surface | p. 92 |
Velocity of a Moving Curve | p. 94 |
Thomas' Derivative and Other Formulae | p. 95 |
Differentiation Formulae | p. 96 |
Balance Laws | p. 101 |
Entropy Inequality and Gibbs Potential | p. 106 |
Other Balance Equations | p. 109 |
Integral Form of Maxwell's Equations | p. 111 |
Phase Equilibrium | p. 113 |
Boundary Value Problems in Phase Equilibrium | p. 113 |
Some Phenomenological Results of Changes in State | p. 114 |
Equilibrium of Fluid Phases with a Planar Interface | p. 117 |
Equilibrium of Fluid Phases with a Spherical Interface | p. 119 |
Variational Formulation of Phase Equilibrium | p. 122 |
Phase Equilibrium in Crystals | p. 125 |
Wulff's Construction | p. 130 |
Stationary and Time-Dependent Phase Changes | p. 133 |
The Problem of Continuous Casting | p. 133 |
On the Evolution of the Solid-Liquid Phase Change | p. 138 |
On the Evolution of the Liquid-Vapor Phase Change | p. 142 |
The Case of a Perfect Gas | p. 146 |
An Introduction to Mixture Theory | p. 149 |
Balance Laws | p. 150 |
Classical Mixtures | p. 155 |
Nonclassical Mixtures | p. 159 |
Balance Equations of Binary Fluid Mixtures | p. 161 |
Constitutive Equations | p. 163 |
Phase Equilibrium and Gibbs' Principle | p. 167 |
Evaporation of a Fluid into a Gas | p. 168 |
Electromagnetism in Matter | p. 171 |
Integral Balance Laws | p. 171 |
Electromagnetic Fields in Rigid Bodies at Rest | p. 174 |
Constitutive Equations for Isotropic Rigid Bodies | p. 178 |
Approximate Constitutive Equations for Isotropic Bodies | p. 180 |
Maxwell's Equations and the Principle of Relativity | p. 181 |
Quasi-electrostatic and Quasi-magnetostatic Approximations | p. 185 |
Balance Equations for Quasi-electrostatics | p. 189 |
Isotropic and Anisotropic Constitutive Equations | p. 192 |
Polarization Fields and the Equations of Quasi-electrostatics | p. 194 |
More General Constitutive Equations | p. 197 |
Lagrangian Formulation of Quasi-electrostatics | p. 198 |
Variational Formulation for Equilibrium in Quasi-electrostatics | p. 201 |
Introduction to Magnetofluid Dynamics | p. 205 |
An Evolution Equation for the Magnetic Field | p. 205 |
Balance Equations in Magnetofluid Dynamics | p. 207 |
Equivalent Form of the Balance Equations | p. 208 |
Constitutive Equations | p. 211 |
Ordinary Waves in Magnetofluid Dynamics | p. 212 |
Alfven's Theorems | p. 216 |
Laminar Motion Between Two Parallel Plates | p. 217 |
Law of Isorotation | p. 222 |
Continua with an Interface and Micromagnetism | p. 225 |
Ferromagnetism and Micromagnetism | p. 225 |
A Ferromagnetic Crystal as a Continuum with an Interface | p. 227 |
Variations in Surfaces of Discontinuity | p. 228 |
Variational Formulation of Weiss Domains | p. 229 |
Weiss Domain Structure | p. 231 |
Weiss Domains in the Absence of a Magnetic Field | p. 234 |
Weiss Domains in Uniaxial Crystals | p. 236 |
A Variational Principle for Elastic Ferromagnetic Crystals | p. 239 |
Weiss Domains in Elastic Uniaxial Crystals | p. 241 |
A Possible Weiss Domain Distribution in Elastic Uniaxial Crystals | p. 243 |
A More General Variational Principle | p. 244 |
Weiss Domain Branching | p. 250 |
Weiss Domains in an Applied Magnetic Field | p. 252 |
Relativistic Continuous Systems | p. 257 |
Lorentz Transformations | p. 257 |
The Principle of Relativity | p. 261 |
Minkowski Spacetime | p. 264 |
Physical Meaning of Minkowski Spacetime | p. 268 |
Four-Dimensional Equation of Motion | p. 270 |
Integral Balance Laws | p. 272 |
The Momentum-Energy Tensor | p. 274 |
Fermi and Fermi-Walker Transport | p. 277 |
The Space Projector | p. 281 |
Intrinsic Deformation Gradient | p. 283 |
Relativistic Dissipation Inequality | p. 286 |
Thermoelastic Materials in Relativity | p. 289 |
About the Physical Meanings of Relative Quantities | p. 293 |
Maxwell's Equation in Matter | p. 295 |
Minkowski's Description | p. 297 |
Ampere's Model | p. 298 |
Brief Introduction to Weak Solutions | p. 301 |
Weak Derivative and Sobolev Spaces | p. 301 |
A Weak Solution of a PDE | p. 305 |
The Lax-Milgram Theorem | p. 307 |
Elements of Surface Geometry | p. 309 |
Regular Surfaces | p. 309 |
The Second Fundamental Form | p. 311 |
Surface Gradient and the Gauss Theorem | p. 316 |
First-Order PDE | p. 319 |
Monge's Cone | p. 319 |
Characteristic Strips | p. 321 |
Cauchy's Problem | p. 324 |
The Tensor Character of Some Physical Quantities | p. 327 |
References | p. 331 |
Index | p. 345 |
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