A first course in rational continuum mechanics
著者
書誌事項
A first course in rational continuum mechanics
（Pure and applied mathematics, 71-1）
Academic Press, 1977
- v. 1. General concepts
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注記
Earlier version published in French in 1973 has title: Introduction à la méchanique rationelle des milieux
Includes bibliographical references and index
内容説明・目次
内容説明
A First Course in Rational Continuum Mechanics, Volume 1: General Concepts describes general concepts in rational continuum mechanics and covers topics ranging from bodies and forces to motions and energies, kinematics, and the stress tensor. Constitutive relations are also discussed, and some definitions and theorems of algebra, geometry, and calculus are included. Exercises and their solutions are given as well. Comprised of four chapters, this volume begins with an introduction to rational mechanics by focusing on the mathematical concepts of bodies, forces, motions, and energies. Systems that provide possible universes for mechanics are described. The next chapter explores kinematics, with emphasis on bodies, placements, and motions as well as other relevant concepts like local deformation and homogeneous transplacement. The book also considers the stress tensor and Cauchy's fundamental theorem before concluding with a discussion on constitutive relations. This monograph is designed for students taking a course in mathematics or physics.
目次
Preface
Contents of Future Volumes
Part 1 General Concepts
Chapter I Bodies, Forces, Motions, and Energies
1. Rational Mechanics
2. Bodies in General
3. Examples of Universes
4. Mass
5. Force
6. The Event World. Framings
7. Motions
8. Linear Momentum. Rotational Momentum. Kinetic Energy. Working. Torque
9. Changes of Frame
10. Rigid Motion
11. Frame-Indifference
12. Axioms of Mechanics
13. The Axioms of Inertia.
14. Euler's Laws of Motion Energy
General References
Chapter II Kinematics
1. Bodies, Placements, Motions
2. Mass-Density
3. Reference Placement. Transplacement
4. Descriptions of Motion
5. Local Deformation
6. Material Time Rates and Gradients in the Spatial Description. Material Surfaces. Kinematic Boundaries
7. Change of Reference Placement
8. Present Placement as Reference
9. Stretch and Rotation
10. Histories
11. Stretching and Spin
12. Homogeneous Transplacement
13. Rates of Change of Integrals Over Material Lines, Surfaces, and Regions. Material Vector Lines. The Vorticity Theorems of Helmholtz and Kelvin
14. Changes of Frame. Frame-Indifference
General References
Chapter III The Stress Tensor
1. Forces and Torques. The Laws of Dynamics. Body Forces and Contact Forces
2. Reactions Upon Containers and Submerged Obstacles
3. The Traction Field. Cauchy's Postulate and the Hamel-Noll Theorem
4. Cauchy's Fundamental Theorem: Existence of the Stress Tensor
5. The General Balance
6. Cauchy's Laws of Motion
7. Mean Values and Lower Bounds for the Stress Field
8. Load. Boundary Condition of Traction
9. Motion of a Free Body
General References
Chapter IV Constitutive Relations
1. Dynamic Processes
2. Constitutive Relations. Noll's Axioms
3. Simple Materials
4. Some Classical Special Cases. Specimens of the Effect of the Axiom of Frame-Indifference
5. Frame-Indifference. Reduced Constitutive Relations
6. Internal Constraints
7. Principle of Determinism for Constrained Simple Materials
8. Equations of Motion for Simple Bodies
9. Homogeneous Transplacements of Unconstrained Simple Bodies
10. Homogeneous Transplacements of Incompressible Simple Bodies
11. Material Isomorphisms
12. The Peer Group
13. Comparison of Peer Groups with Respect to Different Reference Placements
14. Isotropic Materials
15. Solids
16. Fluids
17. Fluid Crystals
18. Motions with Constant Principal Relative Stretch Histories
19. Reduction of the Constitutive Relation for a Simple Material in a Motion with Constant Principal Relative Stretch Histories
General References
Appendix I General Scheme of Notation
Appendix II Some Definitions and Theorems of Algebra, Geometry, and Calculus
A. Algebra
B. Geometry
C. Calculus
Appendix III Solutions of the Exercises
Index
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