- 510 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Classical Continuum Mechanics
About this book
This book provides physical and mathematical foundation as well as complete derivation of the mathematical descriptions and constitutive theories for deformation of solid and fluent continua, both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contra-variant bases. Definitions of co- and contra-variant tensors and tensor calculus are introduced using curvilinear frame and then specialized for Cartesian frame. Both Galilean and non-Galilean coordinate transformations are presented and used in establishing objective tensors and objective rates. Convected time derivatives are derived using the conventional approach as well as non-Galilean transformation and their significance is illustrated in finite deformation of solid continua as well as in the case of fluent continua.
Constitutive theories are derived using entropy inequality and representation theorem. Decomposition of total deformation for solid and fluent continua into volumetric and distortional deformation is essential in providing a sound, general and rigorous framework for deriving constitutive theories. Energy methods and the principle of virtual work are demonstrated to be a small isolated subset of the calculus of variations. Differential form of the mathematical models and calculus of variations preclude energy methods and the principle of virtual work. The material in this book is developed from fundamental concepts at very basic level with gradual progression to advanced topics.
This book contains core scientific knowledge associated with mathematical concepts and theories for deforming continuous matter to prepare graduate students for fundamental and basic research in engineering and sciences. The book presents detailed and consistent derivations with clarity and is ideal for self-study.
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Information
Table of contents
- Cover Page
- Half-Title Page
- Series Page
- Title Page
- Copyright Page
- Dedication Page
- Contents
- Preface
- About the Author
- List of Abbreviations
- 1 Introduction
- 2 Concepts and Mathematical Preliminaries
- 3 Kinematics of Motion, Deformation and Their Measures
- 4 Definitions and Measures of Stresses
- 5 Rates, Convected Time Derivatives and Objectivity
- 6 Conservation and Balance Laws in Eulerian Description
- 7 Conservation and Balance Laws in Lagrangian Description
- 8 Constitutive Theories
- 9 Constitutive Theories for Thermoelastic Solids
- 10 Constitutive Theories for Thermoviscoelastic Solids Without Memory
- 11 Constitutive Theories for Thermoviscoelastic Solids With Memory
- 12 Constitutive Theories for Thermoviscous Fluids
- 13 Constitutive Theories for Thermoviscoelastic Fluids
- 14 Constitutive Theories for Thermo Hypo-Elastic Solids
- 15 Thermodynamic Relations and Complete Mathematical Models
- 16 Energy Methods, Principle of Virtual Work, Calculus of Variations
- Appendix A: Combined Generators and Invariants
- Appendix B: Transformations and Operations in Cartesian, Cylindrical and Spherical Coordinate Systems
- Bibliography
- Index