The Non-Linear Field Theories of Mechanics (3rd ed. 2004. 600 p. w. figs. 25 cm)

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The Non-Linear Field Theories of Mechanics (3rd ed. 2004. 600 p. w. figs. 25 cm)

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  • 製本 Hardcover:ハードカバー版/ページ数 600 p.
  • 商品コード 9783540027799

基本説明

Has become a classic treatise in the field of continuum mechanics. Main parts are: The General Theory of Material Behavior- Elasticity- Fluidity. This edition includes the corrections made by the late C. Truesdell in his personal copy.

Full Description


This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monograph`s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also has greatly contributed to the unification and standardization of the concepts, terms and notations in the field.

Table of Contents

Publisher's Note                                   v
The Genesis of the Non-Linear Field Theories of
Mechanics
Walter Noll vii
Preface to the Third Edition
Stuart S. Antman xiii
Preface to the Second Edition xxiii
The Non-Linear Field Theories of Mechanics. By 1 (541)
C. Truesdell, Professor of Rational Mechanics,
The Johns Hopkins University, Baltimore,
Maryland (USA) and W. Noll, Professor of
Mathematics, Carnegie Institute of Technology,
Pittsburgh, Pennsylvania (USA). (With 28
Figures)
A. Introduction 1 (19)
1. Purpose of the non-linear theories 1 (2)
2. Method and program of the non-linear 3 (2)
theories
3. Structure theories and continuum theories 5 (3)
4. General lines of past research on the 8 (3)
field theories of mechanics
5. The nature of this treatise 11 (2)
6. Terminology and general scheme of 13 (7)
notation
6 A. Appendix. Cylindrical and 19 (1)
spherical co-ordinates
B. Tensor functions 20 (16)
I. Basic concepts 20 (7)
7. Definitions 20 (2)
8. Invariants and isotropic tensor 22 (2)
functions
9. Gradients of tensor functions 24 (3)
II. Representation theorems 27 (9)
10. Representation of invariants of one 27 (2)
symmetric tensor
11. Representation of simultaneous 29 (3)
invariants
12. Tensor functions of one variable 32 (2)
13. Tensor and vector functions of 34 (2)
several variables
C. The general theory of material behavior 36 (81)
14. Scope and plan of the chapter 36 (1)
I. Basic principles 37 (11)
15. Bodies and motions 37 (2)
16. Forces and Stresses 39 (2)
17. Changes of frame. Indifference 41 (2)
18. Equivalent processes 43 (1)
19. The principle of material 44 (1)
frame-indifference
19 A. Appendix. History of the 45 (2)
principle of material frame-indifference
20. The main open problem of the theory 47 (1)
of material behavior
II. Kinematics 48 (8)
21. Deformation 48 (3)
22. Localizations. Local configurations. 51 (1)
Histories
23. Stretch and rotation 52 (1)
24. Stretching and spin 53 (2)
25. Polynomial expressions for the rates 55 (1)
III. The general constitutive equation 56 (36)
26. The principle of determinism. The 56 (2)
general constitutive equation
27. Material isomorphisms. Homogeneity 58 (2)
28. Simple materials, materials of grade 60 (6)
n, dimensional invariance
29. Reduced constitutive equations 66 (3)
30. Internal constraints, 69 (7)
incompressibility, inextensibility
31. The isotropy group 76 (3)
32. Simple fluids 79 (2)
33. Simple solids 81 (5)
33. bis. Simple subfluids 86 (2)
34. Material connections, inhomogeneity, 88 (4)
curvilinear aeolotropy, continuous
dislocations
IV. Special classes of materials 92 (9)
35. Materials of the differential type 93 (2)
36. Materials of the rate type 95 (3)
37. Materials of the integral type 98 (3)
V. Fading memory 101 (16)
38. The principle of fading memory 101 (5)
39. Stress relaxation 106 (2)
40. Asymptotic approximations 108 (5)
41. Position of the classical theories of 113 (4)
viscosity and visco-elasticity
D. Elasticity 117 (309)
42. Scope and plan of the chapter 117 (2)
I. Elastic materials 119 (1)
a) General considerations 119 (175)
43. Definition of an elastic material 119 (1)
43. A. Appendix. The Piola-Kirchhoff 124 (1)
stress tensors
44. Formulation of boundary-value problems 125 (6)
45. The elasticities of an elastic 131 (2)
material
46. Stoppeli's theorems of the existence, 133 (6)
uniqueness, and analyticity of the
solution of a class of traction
boundary-value problems
47. Isotropic elastic materials, I. 139 (3)
General properties
48. Isotropic elastic materials, II. The 142 (5)
principal stresses and principal forces
49. Incompressible isotropic elastic 147 (1)
materials
50. Elastic fluids and solids. Natural 148 (5)
states
51. Restrictions upon the response 153 (9)
functions, I. Isotropic compressible
materials
52. Restrictions upon the response 162 (9)
functions, II. Compressible materials in
general
53. Restrictions upon the response 171 (1)
functions, III. Incompressible materials
b) Exact solutions of special problems of 171 (1)
equilibrium
54. Homogeneous strain of compressible 171 (8)
elastic bodies
55. Incompressible elastic materials, I. 179 (4)
Homogeneous strain
56. Incompressible elastic materials, II. 183 (3)
Preliminaries for the non-homogeneous
solutions for arbitrary materials
57. Incompressible elastic materials, 186 (11)
III. The non-homogeneous solutions for
arbitrary isotropic materials
58. Incompressible elastic materials, IV. 197 (2)
Non-homogeneous solutions for bodies with
certain kinds of aeolotropy and
inhomogeneity
59. Semi-inverse methods: Reduction of 199 (5)
certain static deformations that depend
upon material properties
60. Plane problems 204 (4)
c) Exact solutions of special problems of 208 (1)
motion
61. Quasi-equilibrated motions of 208 (6)
incompressible bodies
62. Radial oscillations of isotropic 214 (5)
cylinders and spheres
d) Systematic methods of approximation 219 (1)
63. Signorini's expansion 219 (4)
64. Signorini's theorems of compatibility 223 (4)
and uniqueness of the equilibrium solution
65. Rivlin and Topakoglu's interpretation 227 (2)
66. Second-order effects in compressible 229 (12)
isotropic materials
67. Second-order effects in 241 (5)
incompressible isotropic materials
68. Infinitesimal strain superimposed 246 (6)
upon a given strain. I. General equations
68 bis. Infinitesimal strain superimposed 252 (8)
upon a given strain. II. Infinitesimal
stability
69. Infinitesimal strain superimposed 260 (3)
upon a given strain, III. General theory
for isotropic materials
70. Infinitesimal strain superimposed 263 (4)
upon a given strain, IV. Solutions of
special problems
e) Wave propagation 267 (1)
71. General theory of acceleration waves 267 (5)
72. Waves of higher order 272 (1)
73. General theory of plane infinitesimal 273 (5)
progressive waves
74. Waves in isotropic compressible 278 (6)
materials. I. General properties
75. Waves in isotropic compressible 284 (1)
materials. II. The case of hydrostatic
pressure
76. Waves in isotropic compressible 285 (3)
materials. III. Determination of the
stress relation from wave speeds
77. Waves in isotropic compressible 288 (3)
materials. IV. Second-order effects
78. Waves in incompressible materials 291 (3)
II Hyperelastic materials 294 (1)
a) General considerations 294 (61)
79. Thermodynamic preliminaries 294 (2)
80. Perfect materials 296 (2)
81. Thermal equilibrium of simple 298 (3)
materials
82. Definition of a hyperelastic material 301 (1)
82 A. Appendix. History of the theory 304 (1)
of hyperelastic materials in finite
strain
83. Work theorems 304 (3)
84. The strain-energy function 307 (3)
85. The isotropy group of the 310 (4)
strain-energy function. Isotropic
hyperelastic materials, hyperelastic
fluids and solids
85 bis. Hyperelastic subfluids 314 (3)
86. Explicit forms of the stress relation 317 (2)
for isotropic hyperelastic materials
b) General theorems 319 (1)
87. Consequences of restrictions upon the 319 (5)
strain-energy function
88. Betti's theorem. Variational problems 324 (4)
89. Stability 328 (4)
90. Wave propagation 332 (4)
c) Solutions of special problems 336 (1)
91. Ericksen's analysis of the 336 (6)
deformations possible in every isotropic
hyperelastic body
92. Special properties of some exact 342 (2)
solutions for isotropic materials
93. Second-order effects in isotropic 344 (3)
materials
d) Special or approximate theories of 347 (1)
hyperelasticity
94. The nature of special or approximate 347 (2)
theories
95. The Mooney-Rivlin theory for rubber 349 (6)
III. Various generalizations of elasticity 355 (46)
and hyperelasticity
96. Thermo-elasticity 355 (8)
96 bis. Coleman's general thermodynamics 363 (19)
of simple materials
96 ter. Coleman and Gurtin's general 382 (3)
theory of wave propagation in simple
materials
97. Electromechanical theories 385 (4)
98. Polar elastic materials 389 (12)
IV. Hypo-elastic materials 401 (25)
99. Definition of a hypo-elastic material 401 (5)
100. Relation to elasticity 406 (5)
101. Work theorems 411 (2)
102. Acceleration waves 413 (2)
103. Solutions of special problems 415 (11)
E. Fluidity 426 (1)
104. Scope and plan of the chapter 426 (1)
I. Simple fluids 427 (1)
a) General classes of flows 427 (1)
105. The concept of a simple fluid 427 (1)
106. Lineal flows, viscometric flows 429 (1)
107. Curvilineal flows 432 (1)
108. Steady viscometric flows 435 (1)
109. Motions with constant stretch history 438 (1)
110. Dynamical preliminaries for the 440 (1)
exact solutions of special flow problems
b) Special flow problems 441 (1)
111. Problems for lineal flows. Simple 441 (1)
shearing, channel flow, lineal
oscillations
112. Helical flows, I. General equations 445 (1)
113. Helical flows, II. Special cases: 448 (1)
Flows in circular pipes
114. Normal-stress end effects 452 (1)
115. Steady torsional flows 458 (1)
116. Position of the general and 465 (1)
Navier-Stokes theories of viscometry
117. Steady flow through tubes 468 (1)
118. Steady extension 472 (1)
118 his. Special flow problems for 473 (2)
subfluids
c) Special simple fluids 475 (1)
119. The older theories of non-linear 475 (10)
viscosity
119 A. Appendix. Truesdell's theory of 485 (3)
the "Stokesian" fluid
120. Asymptotic approximations, I. Steady 488 (1)
viscometric flows
121. Asymptotic approximations, II. 490 (1)
General flows
122. Secondary flows in tubes 497 (1)
123. Fluids of second grade 504 (9)
II. Other fluids 513 (1)
124. Korteweg's theory of capillarity 513 (1)
125. Truesdell's theory of the 515 (1)
"Maxwellian" fluid
126. Anisotropic solids capable of flow 520 (1)
127. The anisotropic fluids of Ericksen, 523 (1)
I. General theory
128. The anisotropic fluids of Ericksen, 528 (1)
II. Statics
129. The anisotropic fluids of Ericksen, 530 (1)
III. Special flows
130. Theories of diffusion 537 (5)
General references 542 (1)
List of works cited 542 (36)
Addendum 578 (2)
Sachverzeichnis (Deutsch-Englisch) 580 (11)
Subject-Index (English-German) 591