A First Course in Rational Continuum Mechanics

A First Course in Rational Continuum Mechanics

General Concepts

1st Edition - January 28, 1977

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  • Author: C. Truesdell
  • eBook ISBN: 9781483220482

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Description

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.

Table of Contents


  • 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

Product details

  • No. of pages: 304
  • Language: English
  • Copyright: © Academic Press 1977
  • Published: January 28, 1977
  • Imprint: Academic Press
  • eBook ISBN: 9781483220482

About the Author

C. Truesdell

About the Editors

Samuel Eilenberg

Affiliations and Expertise

Columbia University

Hyman Bass

Affiliations and Expertise

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

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