Continuum Physics V4

1st Edition - January 28, 1976
Author: A. Cemal Eringen
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 4 0 6 0 - 7

Continuum Physics, Volume IV: Polar and Nonlocal Field Theories discusses the exposition of field theories for bodies which possess inner structure that can interact with… Read more

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Continuum Physics, Volume IV: Polar and Nonlocal Field Theories discusses the exposition of field theories for bodies which possess inner structure that can interact with mechanical and electromagnetic fields. This book provides precise presentations of exact continuum theories on materially non-uniform or non-simple bodies that can respond to short- and long-range inter-particle loads and fields. This volume consists of three parts. Part I is devoted to the study of continuum field theories for bodies having inner structure. All materials, to some extent, are composed of particles that behave like small rigid bodies or deformable particles, unlike the geometrical points of the classical continuum theory. The developments of nonlocal theories of nonpolar and polar continua are covered in Parts II and III. This publication is valuable to students and researchers interested in polar and nonlocal field theories.

List of Contributors

Preface

Contents of Previous Volumes

Part I. Polar Field Theories

Introduction

1. Micropolar Continua

1.1 Scope of the Chapter

1.2 Kinematics

1.3 Strains

1.4 Balance Laws

1.5 Constitutive Theory and Thermodynamics

1.6 Micropolar Elasticity

1.7 Micropolar Fluid Dynamics

2. Micromorphic Continua

2.1 Scope of the Chapter

2.2 Kinematics

2.3 Strains

2.4 Balance Laws

2.5 Spatial Forms of the Balance Laws

2.6 Constitutive Theory and Thermodynamics

2.7 Microelasticity

2.7 Microfluids

3.Higher-Order Micromorphic Continua

3.1 Scope of the Chapter

3.2 Kinematics

3.3 Strain Measures

3.4 Balance Laws

3.5 Micromorphic Elasticity

References

Part II. Nonlocal Field Theories

Introduction

1. Global Balance Laws and Variational Formulations

1.1 Scope of the Section

1.2 Global Statements and the Passage to Local Laws

1.3 Conservation of Mass

1.4 Balance of Linear Momentum

1.5 Balance of Moment of Momentum

1.6 Balance of Energy

1.7 Summary of Results for Thermomechanical Systems

1.8 Conservation of Charge and Magnetic Flux

1.9 Variational Considerations and Carrier Fields

1.10 Invariance, Conservation, and Balance

1.11 Protoelasticity, a Simple Nonlocal Variational Theory

2. Constitutive Theory and Related Topics

2.1 Scope of the Section

2.2 Determinism, Thermodynamics, and Constitutive Equations

2.3 Internal Energy and Entropy

2.4 Combination of the Internal and External Energy Equations

2.5 Invariance under Superimposed Rigid Body Motions

2.6 Entropy Production and the Second Law

2.7 Onsagerian Irreversible Thermodynamics of Nonlinear Continua

2.8 An Alternative Approach: Complete Solutions of the Clausius-Duhem Inequality

2.9 Variational Theories

2.10 Examples

2.11 Appendix: Variational Inferences

References

Part III. Nonlocal Polar Field Theories

Introduction

1. Scope of Part III

2. Balance Laws

3. Constitutive Assumptions

4. Constitutive Equations of Nonlocal Micropolar Elastic Solids

5. Linear Theory of Nonlocal Micropolar Elasticity

6. Field Equations

7. Nonlocal Elasticity

8. Examples of Nonlocal Effects

9. Nonlocal Micropolar Fluids

10. Linear Theory of Nonlocal Micropolar Fluids

11. Field Equations 262

12. Nonlocal Fluid Dynamics

13. Surface Tension

References

Index