Book description
Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study.- Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics
- Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures
- Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors’ own research
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- PART I: THE BEGINNING
-
PART II: KINEMATICS, KINETICS, AND THE FUNDAMENTAL LAWS OF MECHANICS AND THERMODYNAMICS
-
Chapter 3: Kinematics: Motion and Deformation
- Abstract
- 3.1 Body, configuration, motion, displacement
- 3.2 Material derivative, velocity, acceleration
- Exercises
- 3.3 Deformation and strain
- Exercises
- Exercises
- Exercises
- 3.4 Velocity gradient, rate of deformation tensor, vorticity tensor
- Exercises
- 3.5 Material point, material line, material surface, material volume
- 3.6 Volume elements and surface elements in volume and surface integrations
-
Chapter 4: The Fundamental Laws of Thermomechanics
- Abstract
- 4.1 Mass
- 4.2 Forces and moments, linear and angular momentum
- 4.3 Equations of motion (mechanical conservation laws)
- 4.4 The first law of thermodynamics (conservation of energy)
- 4.5 The transport and localization theorems
- Exercises
- 4.6 Cauchy stress tensor, heat flux vector
- 4.7 The energy theorem and stress power
- 4.8 Local forms of the conservation laws
- Exercises
- 4.9 Lagrangian forms of the integral conservation laws
- 4.10 Piola-kirchhoff stress tensors, referential heat flux vector
- Exercises
- 4.11 The lagrangian form of the energy theorem
- 4.12 Local conservation laws in lagrangian form
- Exercises
- 4.13 The second law of thermodynamics
- Exercises
-
Chapter 3: Kinematics: Motion and Deformation
- PART III: CONSTITUTIVE MODELING
-
PART IV: BEYOND MECHANICS AND THERMOMECHANICS
-
Chapter 9: Modeling of Thermo-Electro-Magneto-Mechanical Behavior, with Application to Smart Materials
- Abstract
- 9.1 The fundamental laws of continuum electrodynamics: integral forms
- Exercises
- 9.2 The fundamental laws of continuum electrodynamics: pointwise forms
- Exercises
- Exercises
- 9.3 Modeling of the effective electromagnetic fields
- Exercise
- 9.4 Modeling of the electromagnetically induced coupling terms
- Exercises
- 9.5 Thermo-electro-magneto-mechanical process
- 9.6 Constitutive model development for thermo-electro-magneto-elastic materials: large-deformation theory
- Exercise
- Exercise
- Exercises
- 9.7 Constitutive model development for thermo-electro-magneto-elastic materials: small-deformation theory
- 9.8 Linear, reversible, thermo-electro-magneto-mechanical processes
- 9.9 Specialization of the small-deformation thermo-electro-magneto-elastic framework to piezoelectric materials
- Exercise
-
Chapter 9: Modeling of Thermo-Electro-Magneto-Mechanical Behavior, with Application to Smart Materials
- Appendix A: Different Notions of Invariance
- Appendix B: The Physical Basis of Constitutive Assumptions
- Appendix C: Isotropic Tensors
- Appendix D: A Family of Thermomechanical Processes
- Appendix E: Energy Formulations and Stability Conditions for Newtonian Fluids
- Appendix F: Additional Energy Formulations for Thermo-Electro-Magneto-Mechanical Materials
- Bibliography
- Index
Product information
- Title: Fundamentals of Continuum Mechanics
- Author(s):
- Release date: December 2014
- Publisher(s): Academic Press
- ISBN: 9780123948342
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