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PART III: CONSTITUTIVE MODELING
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PART III: CONSTITUTIVE MODELING
by Robert Lowe, Stephen Bechtel
Fundamentals of Continuum Mechanics
Cover image
Title page
Table of Contents
Copyright
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
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4.8 Local forms of the conservation laws
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Chapter 5: Constitutive Modeling in Mechanics and Thermomechanics
PART III
CONSTITUTIVE MODELING
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