Continuum Physics

Mixtures and EM field Theories

1st Edition - January 28, 1976
Imprint: Academic Press
Editor: A Eringen
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 4 3 1 7 4 8 - 2
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 5 5 5 6 - 4

Continuum Physics, Volume III: Mixtures and EM Field Theories discusses the field theories for bodies composed of different substances, such as mixtures and interaction of… Read more

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Continuum Physics, Volume III: Mixtures and EM Field Theories discusses the field theories for bodies composed of different substances, such as mixtures and interaction of electromagnetic effects with the deformable bodies. This book aims to present the mathematical foundations of nonlinear mechanical, electrical, and magnetic phenomena that take place in mixtures and materially uniform bodies. This volume consists of three parts. Part I is devoted to the development of the theory of mixtures, including kinematics, balance laws, and constitutive equations for bodies consisting of several different substances. Part II is concerned with the mechanics of deformable bodies interacted by electromagnetic fields. The deformation produced by EM fields, EM fields resulting from the deformation of bodies, and plethora of other physical phenomena arising from mechanical and EM interactions are also covered. Micromagnetism is covered in Part III, including considerations arising from the interaction of strong magnetic fields with the inner structure of the body. This publication is valuable to students and researchers interested in mixtures and EM field theories.

List of Contributors

Preface

Contents of Previous Volumes

Part I. Theory of Mixtures

Introduction

1. Kinematics and Field Equations

1.1 Kinematics and Changes of Frame

1.2 Balance of Mass

1.3 Elements of Stoichiometry

1.4 Balance of Momentum

1.5 Balance of Energy

1.6 Second Axiom of Thermodynamics

1.7 Comments on the Formulation of Mixture Theories

2. Diffusion Theories

2.1 Introduction

2.2 Constitutive Assumptions

2.3 Restrictions Imposed by the Second Axiom of Thermodynamics

2.4 Mixtures of Elastic Materials

2.5 Restrictions Imposed by the Axiom of Material Frame-Indifference

2.6 Restrictions Imposed by Material Symmetry

2.7 Mixtures of Gases. Linearized Constitutive Equations

2.8 Mixtures of Gases. Classical Diffusion Theories

2.9 Mixture of a Gas and an Isotropie Solid. Porous Media Model

2.10 Wave Propagation with Diffusion

2.11 Concluding Remarks

References

Part II. Relativistic Continuum Physics: Electromagnetic Interactions

Introduction

1. Electromagnetic Interactions with Deformable Bodies

1.1 Scope of the Section

1.2 A Physical Model

1.3 Balance Laws

1.4 The Second Law of Thermodynamics

1.5 Constitutive Equations for Elastic Materials

1.6 Classical Forms of Constitutive Equations

1.7 Maxwell's Equations in the Material Coordinate System

1.8 Variational Principles for Electromagnetic Elastic Solids

2. Viscoelastic Dispersive Dielectrics

2.1 Scope of the Section

2.2 Basic Assumptions for a Deformable Dielectric

2.3 Constitutive Equations

2.4 Constitutive Equations of Photoviscoelasticity

2.5 Frame Indifference and Material Symmetry

2.6 Propagation of Light in a Rotating Simple Fluid

2.7 Birefringence of a Simple Shear Flow

2.8 Deformations Slow Compared to Electromagnetic Variations

3. Electromagnetic Interactions with Deformable Bodies: Relativistic Case

3.1 Scope of the Section

3.2 Relativistic Kinematics

3.3 Relativistically Invariant Balance Laws

3.4 Relativistic Form of the Second Law of Thermodynamics

3.5 Relativistic Form of the Constitutive Theory

3.6 Nonrelativistic Form of the Theory

3.7 Approximate Theories

References

Part III. Relativistic Continuum Physics: Micromagnetism

Introduction

List of Symbols

1. Physical Background

1.1 Experimental Observations

1.2 The Interactions and Their Continuous Representation

1.3 The Magnetic Spin

2. Relativistic Invariant Theory

2.1 Introduction

2.2 Variational Principle

2.3 Remarks

2.4 Summary of Equations

2.5 Reduced Forms of the Constitutive Equations

2.6 Other Relativistic Approaches

2.7 Conclusion

3. Classical Theory of Micromagnetism

3.1 Introduction

3.2 Global Balance Laws

3.3 Local Field Equations

3.4 Nonlinear Elastic Solids

3.5 A Variational Principle

3.6 Analogy with Oriented and Micropolar Media Theories

3.7 Temperature Fluctuations

3.8 The Classical Theory as Limit of the Relativistic Theory

3.9 The Einstein-De Haas Effect for a Body as a Whole

4. Different Classes of Elastic Materials

4.1 Introduction

4.2 The Principle of Objectivity

4.3 Anisotropie Magnetically Saturated Media

4.4 Material Symmetry

4.5 Nonlinear Hemitropic Magnetoelastic Solids

4.6 Approximations, Infinitesimal Deformations

5. Conclusion

Appendix: The Ponderomotive Force and Couple in a Magnetized Medium

References

Index

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health

Continuum Physics

Mixtures and EM field Theories

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