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# A First Course in Rational Continuum Mechanics

## General Concepts

- 1st Edition - January 28, 1977
- Author: C. Truesdell
- Editors: Samuel Eilenberg, Hyman Bass
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 2 0 4 8 - 2

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… Read more

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Request a sales quoteA 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.

PrefaceContents of Future VolumesPart 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 ReferencesAppendix I General Scheme of NotationAppendix II Some Definitions and Theorems of Algebra, Geometry, and Calculus A. Algebra B. Geometry C. CalculusAppendix III Solutions of the ExercisesIndex

- No. of pages: 304
- Language: English
- Edition: 1
- Published: January 28, 1977
- Imprint: Academic Press
- eBook ISBN: 9781483220482

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### Samuel Eilenberg

Affiliations and expertise

Columbia UniversityHB

### Hyman Bass

Affiliations and expertise

Department of Mathematics, Columbia University, New York, New York