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Fundamentals of Continuum Mechanics,

Edition 1 With Applications to Mechanical, Thermomechanical, and Smart Materials

Editors: By Stephen Bechtel and Robert Lowe

Publication Date: 05 Nov 2014

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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.

Key Features

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

About the author

By Stephen Bechtel, Professor Emeritus in the Department of Mechanical & Aerospace Engineering at The Ohio State University and Robert Lowe, Presidential Fellow in the Department of Mechanical & Aerospace Engineering at The Ohio State University

Dedication
Preface
- Continuum Mechanics: The New Pedagogy
- Acknowledgments
PART I: THE BEGINNING
- Chapter 1: What Is a Continuum?
  - Abstract
- Chapter 2: Our Mathematical Playground
  - Abstract
  - 2.1 Real numbers and euclidean space
  - 2.2 Tensor algebra
  - 2.3 Eigenvalues, eigenvectors, polar decomposition, invariants
  - 2.4 Tensors of order three and four
  - 2.5 Tensor calculus
  - 2.6 Curvilinear coordinates
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
PART III: CONSTITUTIVE MODELING
- Chapter 5: Constitutive Modeling in Mechanics and Thermomechanics
  - Abstract
  - Part I: Mechanics
  - Part II: Thermomechanics
  - 5.3 Fundamental laws, constitutive equations, thermomechanical processes
  - Exercises
  - 5.4 Restrictions on the constitutive equations
  - Exercises
- Chapter 6: Nonlinear Elasticity
  - Abstract
  - 6.1 Mechanical theory
  - 6.2 Thermomechanical theory
  - Exercises
  - Exercises
  - 6.3 Strain energy models
- Chapter 7: Fluid Mechanics
  - Abstract
  - 7.1 Mechanical theory
  - Exercises
  - Exercises
  - 7.2 Thermomechanical theory
  - Exercises
  - Exercises
- Chapter 8: Incompressibility and Thermal Expansion
  - Abstract
  - 8.1 Introduction
  - 8.2 Newtonian fluids
  - Exercise
  - Exercises
  - Exercises
  - Exercises
  - Exercises
  - Exercises
  - Exercise
  - 8.3 Nonlinear elastic solids
  - Exercises
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
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
- E.1 Governing equations
- E.2 Stability conditions
Appendix F: Additional Energy Formulations for Thermo-Electro-Magneto-Mechanical Materials
- F.1 Deformation-temperature-electric displacement-magnetic induction formulation
Bibliography
Index

ISBN: 9780123946003

Page Count: 340

Retail Price :

Lai/Rubin/Krempl, Introduction to Continuum Mechanics 4^th Edition, BH 2010, Hardcover, 608 pgs, 978-0750685603, $97.95
Sadd, Elasticity: Theory, Applications and Numerics 2^nd Edition, AP 2009, Hardcover, 552 pgs, 978-0-12-374446-3, $99.95
Koppel & Oja, Continuum Mechanics, Nova Science Publishers Inc 2010, Hardcover 333 pgs, 978-1607415855, $120.99

Engineers and scientists involved in mathematical and computational modeling in solid mechanics, fluid mechanics, thermodynamics, and materials science; graduate students in engineering, physics, applied mathematics, and materials science.