Eringen Continuum Mechanics of Single-Substance Bodies

1. Auflage 2013
ISBN: 978-1-4832-7667-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 632 Seiten, Web PDF

Continuum Physics, Volume II: Continuum Mechanics of Single-Substance Bodies discusses the continuum mechanics of bodies constituted by a single substance, providing a thorough and precise presentation of exact theories that have evolved during the past years. This book consists of three parts-basic principles, constitutive equations for simple materials, and methods of solution. Part I of this publication is devoted to a discussion of basic principles irrespective of material geometry and constitution that are valid for all kinds of substances, including composites. The geometrical notions, kinematics, balance laws, and thermodynamics of continua are also deliberated. Part II focuses on materials consisting of a single substance, followed by a general theory of constitutive equations and special types of bodies. The thermoelastic solids, thermoviscous fluids, and memory-dependent materials are likewise considered. Part III is devoted to a discussion of a variety of nonlinear and linear problems, as well as nonlinear deformations of elastic solids, viscometric fluids, singular surfaces and waves, and complex function technique. This volume is a good source for researchers and students conducting work on the continuum mechanics of single-substance bodies.

Autoren/Hrsg.

Eringen, A. Cemal

Inhaltsverzeichnis

1;Front Cover;1
2;Continuum Mechanics of Single-Substance Bodies;4
3;Copyright Page;5
4;Table of Contents;6
5;LIST OF CONTRIBUTORS;12
6;PREFACE;14
7;CONTENTS OF VOLUME I;16
8;PART I: BASIC PRINCIPLES;20
8.1;CHAPTER 1. DEFORMATION AND MOTION;22
8.1.1;1.1 Scope of the Chapter;22
8.1.2;1.2 Coordinates;23
8.1.3;1.3 The Motion, Deformation, Strain Measures;30
8.1.4;1.4 Length and Angle Changes;38
8.1.5;1.5 Strain Ellipsoids of Cauchy;43
8.1.6;1.6 Strain Invariants, Principal Directions;47
8.1.7;1.7 Rotation;54
8.1.8;1.8 Area and Volume Changes;59
8.1.9;1.9 Compatibility Conditions;61
8.1.10;1.10 Kinematics, Time Rates of Tensors;64
8.1.11;1.11 Deformation Rate, Spin, Vorticity;69
8.1.12;1.12 Rates of Strains and Rotations;72
8.1.13;1.13 Material and Spatial Manifolds;75
8.1.14;1.14 Kinematics of Line, Surface, and Volume Integrals;78
8.2;CHAPTER 2. BALANCE LAWS;88
8.2.1;2.1 Scope of the Chapter;88
8.2.2;2.2 Global Balance Laws;89
8.2.3;2.3 Master Law for Local Balance;93
8.2.4;2.4 Local Balance Laws;96
8.2.5;2.5 Stress Quadratic, Stress Invariants;104
8.2.6;2.6 Stress Flux;106
8.3;CHAPTER 3. THERMODYNAMICS OF CONTINUA;108
8.3.1;3.1 Scope of the Chapter;108
8.3.2;3.2 Thermodynamic Processes;109
8.3.3;3.3 The First and the Second Laws of Thermodynamics;112
8.3.4;3.4 Thermodynamic Restrictions on Some Simple Materials;116
8.3.5;3.5 Discontinuous Thermodynamic Processes;124
8.3.6;3.6 Thermodynamics of Materials with Memory;129
8.3.7;3.7 Onsager Forces and Fluxes;134
8.3.8;3.8 Onsager Force Potential, Variational Principle;143
8.3.9;References;146
9;PART II: CONSTITUTIVE EQUATIONS FOR SIMPLE MATERIALS;148
9.1;CHAPTER 1. GENERAL THEORY;150
9.1.1;1.1 Scope of the Chapter;150
9.1.2;1.2 Raison d'Etre;151
9.1.3;1.3 Axioms of Constitutive Theory;153
9.1.4;1.4 Thermomechanical Materials;165
9.1.5;1.5 Thermoelastic Materials;172
9.1.6;1.6 Thermoviscous Fluids;174
9.1.7;1.7 Simple Thermomechanical Materials;178
9.1.8;References;191
9.2;CHAPTER 2. THERMOELASTIC SOLIDS;192
9.2.1;2.1 Scope of the Chapter;193
9.2.2;2.2 Résumé of the Fundamental Equations;194
9.2.3;2.3 Constitutive Relations for Thermoelastic Solids;196
9.2.4;2.4 Isotropie Thermoelastic Solids;202
9.2.5;2.5 Linear Constitutive Relations;205
9.2.6;2.6 Linear Theory for Isotropie Thermoelastic Solids;209
9.2.7;2.7 Temperature-Rate-Dependent Thermoelastic Solids;210
9.2.8;2.8 Constitutive Relations for Elastic Materials. Hyperelasticity;218
9.2.9;2.9 Various Forms of Constitutive Relations;222
9.2.10;2.10 Anisotropie Elastic Solids;224
9.2.11;2.11 Restrictions on the Strain Energy Function for Isotropie Materials;239
9.2.12;2.12 Work Relations for Elastic Equilibrium;242
9.2.13;2.13 Formulation of Boundary-Value Problems. Elasticities;244
9.2.14;2.14 Formulation of Boundary-Value Problems in Isotropie Materials;249
9.2.15;2.15 Approximate Theories for Hyperelastic Solids;254
9.2.16;2.16 Variational Theorems of Elastostatics;262
9.2.17;2.17 Small Motions Superimposed on Large Static Deformations;265
9.2.18;2.18 Stability of Elastic Equilibrium;277
9.2.19;References;281
9.3;CHAPTER 3. THERMOVISCOUS FLUIDS;286
9.3.1;3.1 Scope of the Chapter;286
9.3.2;3.2 Equations of Balance;287
9.3.3;3.3 Entropy Inequality;289
9.3.4;3.4 Definition and Constitutive Relations of a Temperature-Rate-Independent Thermoviscous Fluid;291
9.3.5;3.5 Limitations Placed on the Constitutive Functions by the Entropy Inequality;294
9.3.6;3.6 Connection with the Classical Theory of Linear Thermoviscous Fluids;297
9.3.7;References;300
9.4;CHAPTER 4. SIMPLE MATERIALS WITH FADING MEMORY;302
9.4.1;4.1 Scope of the Chapter;303
9.4.2;4.2 Linear Viscoelasticity;305
9.4.3;4.3 Mathematical Prerequisites;314
9.4.4;4.4 Nonlinear Constitutive Relations;320
9.4.5;4.5 Material Symmetries;330
9.4.6;4.6 Fading Memory Space;342
9.4.7;4.7 Finite Linear Viscoelasticity;347
9.4.8;4.8 Materials of Integral Type;355
9.4.9;4.9 Thermodynamics of Kelvin–Voigt Materials;364
9.4.10;4.10 Thermodynamics of Materials with Fading Memory;370
9.4.11;4.11 Thermodynamical Restrictions on the Mechanical Constitutive Relations;376
9.4.12;4.12 Small Deformations;391
9.4.13;4.13 Material Testing;395
9.4.14;4.14 Fluids;406
9.4.15;References;416
10;PART III: METHODS OF SOLUTION;424
10.1;CHAPTER 1. EXACT SOLUTIONS IN FLUIDS AND SOLIDS;426
10.1.1;1.1 Scope of the Chapter;427
10.1.2;1.2 Historical Précis;427
10.1.3;1.3 Erickson's Theorems in Finite Elasticity for Static Deformations;428
10.1.4;1.4 Viscometric Flows;432
10.1.5;1.5 Universal Motions for Isotropie, Homogeneous, Incompressible, Simple Materials;433
10.1.6;1.6 Sundry Mathematical Representation Theorems;435
10.1.7;1.7 Simple Fluids;437
10.1.8;1.8 Simple Shearing in a Reiner–Rivlin Fluid;438
10.1.9;1.9 Simple Shearing in a Simple Fluid;440
10.1.10;1.10 Radial Flow in a Simple Fluid;442
10.1.11;1.11 On the Thermodynamic Impossibility of a Steady Poiseulle Flow in a General Simple Fluid;445
10.1.12;1.12 Simple Isotropie Solids;449
10.1.13;1.13 Dynamic Simple Shearing in an Elastic Body;450
10.1.14;1.14 Motions in Simple Solids; Response Functionals Determined by Homogeneous Motions;453
10.1.15;1.15 Radial Oscillations in a Simple Solid Hollow Sphere;463
10.1.16;1.16 Static Deformations;465
10.1.17;References;466
10.2;CHAPTER 2. SINGULAR SURFACES AND WAVES;468
10.2.1;2.1 Scope of the Chapter;469
10.2.2;2.2 Compatibility Conditions on a Moving Singular Surface;472
10.2.3;2.3 Classification of Singular Surfaces;477
10.2.4;2.4 Basic Laws of Continuum Mechanics;478
10.2.5;2.5 Propagation of Acceleration Waves in Definite Conductors;480
10.2.6;2.6 The Variation of the Amplitudes of Acceleration Waves in Definite Conductors;484
10.2.7;2.7 Propagation of Acceleration Waves in Nonconductors;488
10.2.8;2.8 Acceleration Waves in Isotropie Materials;490
10.2.9;2.9 The Influence of Hydrostatic Pressure on the Propagation of Acceleration Waves;493
10.2.10;2.10 Second-Order Effects in Wave Propagation;496
10.2.11;2.11 Relations of Acceleration Waves to Plane Waves of Infinitesimal Amplitude;498
10.2.12;2.12 Waves in Incompressible Materials;501
10.2.13;2.13 Simple Waves;503
10.2.14;2.14 Unidirectional Simple Waves in Isotropie Media;508
10.2.15;2.15 Shock Waves in Elastic Nonconductors;513
10.2.16;2.16 Shock Waves in Infinitesimal Amplitude;517
10.2.17;2.17 Shock Waves in Isotropie Media;519
10.2.18;2.18 Solution of Initial Boundary Value Problems;522
10.2.19;References;532
10.3;CHAPTER 3. COMPLEX FUNCTION TECHNIQUE;542
10.3.1;3.1 Scope of the Chapter;543
10.3.2;3.2 Definitions: Dual Series, Dual Integral Equations, Potential, Flux;544
10.3.3;3.3 Methods of Solution of Mixed Boundary Value Problems;549
10.3.4;3.4 Direct Application of Complex Potentials;550
10.3.5;3.5 Nature of the Kernel in Mixed Boundary Value Problems;555
10.3.6;3.6 Reduction of Dual Series Equations to Singular Integral Equations;559
10.3.7;3.7 Reduction of Dual Integral Equations to Singular Integral Equations;565
10.3.8;3.8 Dual Integral Equations Leading to Singular Integral Equations of the Second Kind;570
10.3.9;3.9 A System of Dual Series–Integral Equations;580
10.3.10;3.10 Singular Integral Equations with a Generalized Cauchy Kernel;587
10.3.11;3.11 Numerical Solution of the Singular Integral Equations of the First Kind;591
10.3.12;3.12 Solution of Singular Integral Equations of the Second Kind;604
10.3.13;3.13 Solutions by Gauss-Chebyshev and Gauss–Jacoby Integration Formulas;610
10.3.14;References;620
11;AUTHOR INDEX;624
12;SUBJECT INDEX;629