Continuum Physics V4

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